All Summon spells fall under the Conjuration school, which imposes additional restrictions.
Specifically:
A creature or object brought into being or transported to your location by a conjuration spell cannot appear inside another creature or object, nor can it appear floating in an empty space. It must arrive in an open location on a surface capable of supporting it.
This rules out several of your scenarios:
Summoning a frog inside someone's mouth violates the "inside another creature" provision.
Summoning an eel (an aquatic creature) wrapped around a sword hilt violates the "on a surface capable of supporting it" provision.
Most Summon spells also have this provision:
Creatures cannot be summoned into an environment that cannot support them.
This usually rules out the summoning so many horses that it crushes someone idea... If the horses are packed that tightly, it isn't really a horse-friendly environment.
The intent here is pretty clear: The act of summoning is too imprecise and/or slow to use as an attack. Assume you have no more precision than a 5'x5' square, the creature arrives in a neutral pose (or at least one that isn't controlled by the summoner), and that anyone close to the point of summoning can trivially move out of contact.
Making it Work
So let's say that you are running a game and want to allow for pinpoint summoning. There are a few things that you should consider:
How does the player "hit" their pinpoint target?
The common mechanic for this is a reflex save on the part of the victim. If the victim saves, then the summon fails (they've moved the "support" away from the summoning portal). If the victim fails to save, arbitrate the results to taste.
Alternatively, you could have the caster make a ranged touch attack. If you're a simulationist, you may apply a modifier to this attack or use the variant called shot rules.
How do you maintain spell-level balance?
Basically, this is going to eliminate "balance" within the game. The spells are designed with the assumption that you can't do this kind of thing, so they'll allow (for example) poisonous frogs at a relatively low spell level. Some people really like this. Some people don't. The important thing is to understand that things are about to get a little weird.
If I can summon something in a victim's mouth, can I center my fireball on their tonsils?
Allowing one spell to be cast with high precision means you have to consider casting other spells the same way. How you decide this will depend on your campaign style... Does it give a bonus to the reflex save? Does it increase damage? Or does the extra precision apply only to a few amusing spells?
Does the victim feel it happening?
I would say yes. This gives them a save.
If the person closes his mouth while the spell is being cast, will this break the spell?
Yes. It would break Line of Sight, which is required to cast spells. However, they'd need to make a reflex save if they can't perceive you casting.
Speaking as an experienced summoner, this misses the point of summoning completely.
The beauty of summon spells is that you can choose what to summon on the fly.
Listen closely to this secret of D&D - there is no such thing in the game as "straight DPS."
If you want to calculate average damage against some imaginary AC assuming full attacks, go to all the summon monster statblocks and do it yourself, it's self explanatory, you don't need us to do it for you. What Summon Monster 1 creature has the highest DPS? The eagle. Best tanking (assuming you define that as hp)? The pony. Best combination? The dolphin. Of course, the dolphin isn't of much use on the land, and a pony doesn't tank worth crap against flying opponents. And thus you have the crux of the problem.
Most "best DPS" and other such optimization discussions are based on artificial scenarios that have jack to do with real adventuring situations. The strength of a summoner is in bringing the right thing to the battle at hand. You'll want that fire beetle when there's something mind-affecting around. For every situation there are more optimal movement types, attack types, etc. Many choices are effective DPS zero or tanking ineffective in many circumstances regardless of the exercise of taking the average of their damage dice.
Therefore any answer to this question that lists a monster is frankly not only wrong but is causing you to play your character in a sucky way. Don't do it. You have to know ALL the summons at a given level and use the one whose strengths and weaknesses fit the situation.
Allow me to cite the time I was fighting an invisible flying lich behind a wall of force (Caution, spoilers for Rise of the Runelords). I summoned one of the objectively crappiest monsters possible at that level, a musteval guardinal. But as a burrowing critter than can see invisible and fire magic missiles, it could get to him, see him, and damage him, and designate him as a target for the rest of the group. DPS by the stat block about 2.5; DPS in reality "dead lich in one round." DPSing with summoning is like being Doctor Who and deciding your sonic screwdriver is a mace and you're going to try to smack people with it. It misses the point by somewhere around a mile.
Best Answer
So according to Summon Monster:
Which brings the question: can a Native Outsider be Extraplanar?
So yes, while not on the Material Plane, a Native Outsider would have the Extraplanar subtype (Native and Extraplanar are not incompatible), and therefore be a valid target for summoning.
However, Summon Monster has already clearly defined Summon Lists which don't include any Native Outsider, meaning they would have to be adapted. There is also the problem of level: when summoning a monster, you just get the basic one, not a version with classes. So it could be argued that Summoning an Aasimar (for example) would get you the Lvl 0 version. I would see several ways of doing it, but that would definitely be in the houserules domain.
So, while an Outsider (Native) is theoretically a valid target of Summoning in RAW, the actual mechanisms of it would have to be houseruled by the GM.