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
The standard monsters that I could find in the Monster Manual with the ability to cast dispel magic are:
- Death Knight (pg. 47)
- Glabrezu (pg. 58)
- Drider with the spellcasting variant (pg. 120)
- Drow Priestess (pg. 129)
- Lich (pg. 202)
- Mummy Lord (pg. 229)
- Pixie (pg. 253)
- Androsphinx (pg. 281)
- Gynosphinx (pg. 282)
- Mezzoloth (pg. 313)
- Nycaloth (pg. 314)
- Ultroloth (pg. 314)
- And the standard NPC Priest in Appendix B (pg. 348)
Most of these are the kind of monster that would almost certainly attack the party. The NPC Priest might not, but I can't see a reason for a priest to randomly dispel someone's shelter then walk away (unless their god has strong objections to that specific spell, but that seems forced). The sphinxes also don't tend to attack people, but they're rare, completely level-inappropriate, and don't move around much.
The only one of those monsters that I can see randomly dispelling but not attacking is the Pixie. If you read their lore, you can see that they love to troll people without any hostile intent, so this sort of thing is right in their wheelhouse. It also appears to suit your other requirements (easy to kill if it comes to a fight).
Best Answer
Your wizard can do two things: wait to learn the spell or cast the spell by succeeding on a spellcasting check.
Learning the Spell
When you reach 5th level (and gain access to 3rd level spells) you can copy it into your spellbook using the rules on p.114 of the PHB.
Casting the Spell
At any time you can attempt to cast it using the rules on p.200 of the Dungeon Master's Guide (DMG). If you are 5th level you can do this automatically, however:
For a 3rd level spell the DC is 13, so for a 2nd level caster with a 16-17 Intelligence (+5) you need an 8 or better.
Whether you are successful or not the spell is gone and you now have a blank scroll rather than a spell scroll.