First question: trigger
The character needs only to have at least one level of a class which can cast the spell. In this case a first level wizard will be able to trigger any wizard spell.
Second question: completion
From the SRD: Scrolls
To have any chance of activating a scroll spell, the scroll user must meet the following requirements.
- The spell must be of the correct type (arcane or divine). Arcane
spellcasters (wizards, sorcerers, and bards) can only use scrolls
containing arcane spells, and divine spellcasters (clerics, druids,
paladins, and rangers) can only use scrolls containing divine spells.
(The type of scroll a character creates is also determined by his
class.)
- The user must have the spell on her class list.
- The user
must have the requisite ability score. If the user meets all the
requirements noted above, and her caster level is at least equal to
the spell's caster level, she can automatically activate the spell
without a check.
This means that the character must be a spell caster of the correct type (arcane or divine): so no a fighter will not be able to use a scroll.
If she meets all three requirements but her own caster level is lower than the scroll spell's caster level, then she has to make a caster level check (DC = scroll's caster level + 1) to cast the spell successfully.
In this case: yes a first level wizard will be able to try with any arcane scroll (if he has the required Int) but he will have to perform an appropriate caster level with the following consequences:
If she fails, she must make a DC 5 Wisdom check to avoid a mishap (see Scroll Mishaps). A natural roll of 1 always fails, whatever the modifiers. Activating a scroll is a standard action (or the spell's casting time, whichever is longer) and it provokes attacks of opportunity exactly as casting a spell does.
Use magic device
You can use this skill to read a spell or to activate a magic item.
Use Magic Device lets you use a magic item as if you had the spell
ability or class features of another class, as if you were a different
race, or as if you were of a different alignment.
This allow to override the first condition: even if you are not of the correct class (or have the wrong alignment and so on) and you have the use magic device skill you can do a check and try anyway.
So in this case if your 20th level fighter is trained in use magic device: yes he can use a scroll
Identifying a scroll is different from deciphering a scroll and neither requires expending the scroll.
Identifying
The detect magic spell determines if there're any magic auras in the area on the first round, the number of magic auras and the most potent aura in the area on the second, and where exactly those auras are and how powerful each is on the third. With a successful Knowledge (arcana) skill check (DC 15 + spell level), the caster can determine the aura's school of magic; this check apparently takes no time and is part of the 3rd-round detect magic effect. Doing this would tell the caster only the school of the spell or spells on the scroll.
A 3-round thorough examination of the object while employing the detect magic spell permits the caster to "[i]dentify the properties of a magic item" with a successful Spellcraft check (DC 15 + scroll's caster level). This tells the caster everything about the magic item, with apparently one exception. The caster knows whether the scroll is arcane or divine, what level spell is on it, what level the spell or spells are scribed at, and so on, but identifying doesn't reveal exactly what spell is on the scroll; to do that the caster must decipher the scroll.
These 3 rounds are in addition to the first 3 rounds leading to pinpointing each aura in the area of the spell detect magic. Events happen in order unless stated to happen simultaneously.
(The analyze dweomer spell also reveals these properties, but the word dweomer is difficult to say without laughing.)
Deciphering
To find out which spell is on the scroll (and subsequently be able to activate it) the caster must decipher the scroll, which requires a successful full-round Spellcraft skill check (DC 20 + spell level), a successful 1-minute Use Magic Device skill check (DC 25 + spell level), or the read magic spell.
After the scroll's deciphered, that scroll's always deciphered for that caster. No further checks need be made, and the scroll can be employed normally.
Don't conflate identifying with deciphering. The hairs are fine and difficult to split but the game splits them anyway: When a caster identifies an item's properties, he gets command words, number of charges, and so on (pretty much just like he read the item's description from the book) but not the name of the spell on the scroll; the caster gets that and the ability to activate the scroll from deciphering the scroll.
Note: That's weird and the Pathfinder Role-playing Game buries that on page 490: "The writing on a scroll must be deciphered before a character can... know exactly what spell it contains." This also isn't exclusive to Pathfinder--both the Dungeons and Dragons 3.0 and 3.5 Dungeon Master's Guides have the exact same language in their Deciphering a Scroll sections (pages 203 and 238, respectively).
Note: A solid but dangerous case can be made for skipping the identification step if the caster already knows what he's dealing with, much in the same way someone proficient with a sword can just whack fools with the sword instead of learning its maker, properties, and history before he starts using it. The DM rolls secretly to determine if a character deciphers gibberish via the Linguistics skill, but the player rolls openly to decipher a magic scroll via the Spellcraft skill or Use Magic Device skill, so right there the player will know it's a magic scroll and, if successful in deciphering it, know the spell on it. The character can then try to activate the scroll, but--and this is really a DM's call--the character still won't know any of the scroll's properties (such as it's spell level or the scriber's caster level) because the character's not identified the scroll's properties. Just as Fighter Joe can still take swings with a magic sword without knowing its exact properties, Wizard Jim can decipher a scroll and, if he meets the requirements, cast the spell from the scroll without knowing exactly what's going to happen. I've never seen a player want to do that, but I'd totally let him. That could be hilarious.
Other Tidbits: There are spells that straight-up answer questions and get information; one could possibly use those and make a big pile of information about a scroll. There are feats and classes that are scroll-specific, and those might be useful. I've ignored both because they seem to be beyond the question's scope.
Best Answer
You're missing the general rules for scrolls, on page 139 of the DMG.