Yes, there is a potion of Magic Circle against Evil in the DMG.
It would work fine with the first kind of casting (the emanation of protection vs evil) and would move with the target as is normal for the spell.
If you made a "second kind of casting" MCvE potion, it would still work like the spell, go back and read it carefully - it would need to be drunk by a spellcaster one round away from casting a summoning/binding spell, not by the prospective bound creature. The second kind of casting overrides several of the spell's normal parameters in its description. It might be helpful in terms of not depleting a mage's third level spell slot right before summoning something touchy, but not as a "bad guy trap."
Yes, but only via some finagling. A potion/oil only has one target normally, and the imbiber may not select additional targets even if he would be allowed to normally as the caster of the spell. However, a number of spells that can be made into potions affect creatures other than their direct target(s) in some way. None of the methods of doing this involve any decisions normally made by the caster at the time of casting, as:
Potions are like spells cast upon the imbiber. The character taking the potion doesn't get to make any decisions about the effect—the caster who brewed the potion has already done so.
A cursory overview of ways spells do this by means of example follows:
Wandering Star Motes: because this spell can acquire new targets after being brought into effect, it can be used to affect other creatures (though the initial target must be the imbiber).
Enlarge Person: This spell's effect changes how the drinker can affect others in some ways, and so affects them indirectly. This is how most potions work.
Moment of Greatness: This spell is capable of being made into a potion, but also affects those in an area. The area effect functions as normal, and may affect various creatures other than the imbiber.
Draconic Reservoir: This spell gives the subject of the spell the ability to make choices about the spells' effects, including the targets of some possible new effects. These choices may still be able to be made by an imbiber.
Blood Scent: This spell has multiple targets. While the imbiber cannot make use of this, technically the potion's creator could, though things might go badly if the potion was used in the wrong circumstances. In order to target multiple creatures, the creator would need to make all the choices normally made when selecting a target at the time of casting when the potion is made. What those choices are is unclear RAW, but at a minimum includes enough information to uniquely identify who would be affected regardless of when the potion is used.
The imbiber must certainly still be a target, but it is possible that other targets may be added, as target selection is a choice normally made while casting the spell and the rules do not anywhere expressly forbid multi-target potions.
See also: Volatile Vaporizer
Best Answer
Magic oils are complicated by being only lightly detailed
I would be remiss in my duties were I not to point out that technically the feat Brew Potion (Player's Handbook 89) does not allow a creature that possesses it to create magic oils. In fact, nothing seems to allow the creation of magic oils! While this is undoubtedly merely an oversight, it's an oversight that's just quirky enough for a really strict DM to rule that magic oils are the product of ancient and lost civilizations, forgotten magicks, vast power beyond the reach of insignificant mortals, or whatever so as to forbid their creation by PCs. Nonetheless, the responses below assume a DM who permits anyway the creation of magical oils using the feat Brew Potion. (I took the liberty of rephrasing the inquiries present in the questions. I hope that's okay.)
Does the creator of an oil or potion determine if the item is an oil or potion upon the item's creation or upon its use? Upon the item's creation.
The Dungeon Master's Guide Table 7–17: Potions and Oils (230) lists magic oils only as magic oils and potions as only potions, not providing any examples of hybrid magic oil/potions. (Although some spells like the invisibility and levitate spells can be randomly generated as either a magic oil or a potion, no results are listed as a magic oil and a potion.) This leads this reader to believe that a creator must designate his creation as a magic oil or potion upon the item's creation. (Also see below for further magic oil restrictions.)
If the spell offers a choice of how its used, does the creator or the user decide if a magic oil or potion's effect will affect an area or be targeted? The creator… but it's more complicated than that.
This answer needs two parts. First, the Dungeon Master's Guide says
That is, the creator of the magic oil or potion—not the applier or the drinker—makes decisions about the potion or oil's effect (and, obviously, makes those decisions when the item is created). Also, keep in mind that because a potion's consumer is also typically the target of the potion's spell, this makes brewing, for example, a potion of magic missile usually a bad choice except as a prank or trap. (This DM's had the PCs' enemies carry potions of painless death labeled as potions of cure light wounds, for example.)
Second, according to the feat Brew Potion, the spell that's turned into a potion must be one "that targets one or more creatures," so this DM would mandate that, for example, a potion of dispel magic can only be created so that the potion's effect is a targeted dispel rather than an area dispel. Likewise, this DM would extend this ruling to any spell that could affect an area or a target, mandating that when it's turned into a potion the creator must pick the targeted version of the spell.
Are oils used like splash weapons? No.
A magic oil must be smeared upon—not thrown at or splashed on—the subject that's to be affected by it. (Also see below.) The Dungeon Master's Guide says
There are no other rules for the in-combat application of a magic oil. Apparently, for instance, a magic oil container can't be hurled at a foe in hopes of affecting the foe with its contents, and a creature can't smear a magical oil on another conscious creature, no matter how willing that conscious creature may be. Ask the DM if house rules eliminate either of these restrictions—potions and oils are widely considered sub-par, after all.1 (Also see here for more about potion-delivery optimization and here for Pathfinder's similar magic-oils-in-combat rules.)
Can an oil of dispel magic be applied to an object despite the targeting limitations present in the various descriptions of potions? Probably yes.
If a DM allows a creator to create magic oils at all—which this DM does—this fellow DM recommends the following rulings: A creature that possesses the feat Brew Potion (or that can create potions through different but similar means) can also create a magic oil if the spell that's to become a magic oil has as its target one or more objects. Further, this DM recommends the following ruling: A magic oil can only target an object.
To be clear, according to the feat Brew Potion, a spell that's to become a potion must be known by the creator and must target one or more creatures, and the potion's creator makes choices as if he cast the spell when the potion's created. Further, the spell can't have a casting time of 1 min. or more (DMG 229), and the spell can't have a Range entry of Personal (286).
Finally, the Dungeon Master's Guide says, "The person applying an oil is the effective caster, but the object is the target" (229). To this reader that strongly implies that only objects can be affected by magic oils.2 This is borne out by the Dungeon Master's Guide's examples of magic oils: it lists as magic oils only spells that can or also target one or more objects, like the spells magic stone, magic weapon, shillelagh, bless weapon, and even darkness. Based on these examples, this DM's ruled that a magic oil can only be applied to an object.
This reader believes that—despite the light details—the reason magic oils even exist is to add versatility to what can be created with the feat Brew Potion. However, this DM doesn't view a magic oil as just a different delivery method from a potion but a necessity when dealing with object-targeting spells.
"So you wanna huck dispel magic grenades?"
So what happens when a creator decides he's going to make an oil or potion of dispel magic? The creator first picks whether to make a magic oil or a potion. Whether the creator opts for a magic oil or a potion, the creator must pick the dispel magic spell's targeted dispel option. If he picks to make a potion, the spell's effect will affect the drinker as if the drinker had been the subject of the spell. If he picks to make an oil, the spell's effect will affect an object on which the oil has been smeared as if the object had been the subject of the spell (i.e. a successful caster level check renders the magic item nonmagical for 1d4 rounds). Using an oil of dispel magic this way in combat against a conscious and mobile foe's gear is probably too complicated: the DM must concoct house rules to do so, or the DM may simply rule that doing so is impossible. ("No," says the DM, "you can't rub the oil of dispel magic onto the balor's sword while it's wielding it. Move on.")
(This reader suspects that Table 7–17 omits an entry of "dispel magic (oil or potion)" because of the complicated nature of the item rather than because such an item can't be created, but this is pure and total speculation.)
However, if this must be the PC's jam, the Dragon #289 Wizards Workshop: Silicon Sorcery column "Gauntlet: Dark Legacy" on Gauntlet Potions says
(More on the video game Gauntlet: Dark Legacy—from which these items were adapted—can be found here.) This article predates the 3.5 revision, making the material subject to minor adjustments by the DM (see DMG 4). Several Gauntlet potions are described in the article, and, as can be seen by the description above, a DM may allow the creation of new ones. This article should be any grenadier's go-to source for potion grenades.3
However, this reader does caution a DM who's considering allowing them into his campaign that these Gauntlet potions are a way to create multiple spell effects with a single activation, so they're potentially unbalanced if the spells within are allowed without restraint.
1 If a reader's got the idea in his head already, it's definitely possible to read that DMG description of magic oils and assume the DMG is discussing tossing the magic oil at a foe… except that reading's spoiled by that last sentence. That is, if throwing a magic oil at a conscious and mobile creature takes a standard action and has the same efficacy as taking a full-round action to apply a magic oil to an unconscious creature, why not just throw the magic oil at the unconscious creature? While the DMG can make some glaring errors (see below), this reader assumes that the DMG assumes here that a magic oil's user typically takes a standard action to smear a magic oil on himself, sometimes takes a full-round action to smear a magic oil on another creature, and chucks a magic oil so that it affects a foe never.
2 As mentioned, the DMG says, "[I]t takes a full-round action to apply an oil to an unconscious creature," and an oil of speak with dead is mentioned as an example. A DM that allows magic oils to affect dead and unconscious creatures must adjudicate the effects of, for example, a potion of darkness when applied to an unconscious creature. An oil of speak with dead, by the way, is impossible according to the DMG's own rules: A potion or oil "can duplicate the effect of a spell… that has a casting time of less than 1 minute" (ibid.), and the spell speak with dead has a casting time of 10 min. Sigh.
3 For syringe-like projectiles that deliver potion effects and that can be thrown, see the prestige class alchemist savant (Magic of Eberron 53–7) and that class's ability to brew magic spellvials.