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
Yes, you can. Specialization is a Wizard class feature that affects Wizard spellcasting only. It has no effect on spells from other classes. Complete Arcane, for example, explicitly suggests multiclassing with Sorcerer to get your missing spells.
Complete Arcane pg. 185
One way around at least part of this restriction is for a specialist wizard to take levels in sorcerer, using her sorcerer spellcasting ability to master the spells and magic items she cannot use as a wizard.
The FAQ (which is not a real rules source but may be good for convincing DMs) explicitly answered this question as well.
Specialization would be much clearer if they simply said that the spells were removed from your wizard spell list, and even effects that add spells to your spell list cannot add spells of your banned schools to your wizard spell list. That's what all the specialization rules sum up to, they just chose a long and complicated way to describe it.
However, note that Wizards, like all spellcasters, multiclass poorly. Being behind on spell levels is a very serious blow to your power. The addition of lower-level spells from another class is not nearly enough to justify this, from a purely-mechanical perspective. There are exceptions, but they involve dual-progression PrCs that can be entered with only one level lost, and that have their own class features (like Anima Mage from Tome of Magic or Ultimate Magus from Complete Mage).
Best Answer
Switching default male pronoun to default female, in deference to Wizards’ own style and to match rules quotes.
Her wizard class features give her no special ability to activate the item
As she does not have access to Enchantment or Evocation spells, she does not qualify as having those spells on her spell list for the purposes of activating spell-completion and spell-trigger items (e.g. scrolls and wands), even for spells that are otherwise on the wizard spell list. The School Specialization sidebar makes that much, at least, quite clear:
However, Use Magic Device is all about using items you usually can’t
A wizard could use the Use Magic Device skill to activate such items, the same as any other character. Wizards don’t get Use Magic Device in-class and don’t tend to invest heavily in Charisma, but the loremaster prestige class is really easy for a wizard to enter, and would get you Use Magic Device.
Anyway, that a wizard can Use Magic Device on spell-completion and spell-trigger items is, unfortunately, not immediately clear from the rule I quoted: that rule says they are not available, with no qualifications. Unfortunately, Wizards had this tendency, particularly early on, to assume single-classed characters, and ignored cross-class skills. It probably simplified the language, but at the cost of making things confusing when you stepped away from those assumptions.
For this, I am going to draw parallels to the question of whether or not a multiclass specialist wizard may cast spells of her banned school with her other class. The books explicitly allow this (Complete Arcane 185), despite that very same rule I’ve quoted above which seems to say that the specialist wizard may not cast those spells at all. What that line actually means is that the wizard class itself does not give you the ability to cast those spells or use those items when you specialize and ban those schools. You can still use the usual methods around that inability, the same as, say, a monk could.