[RPG] Use-activated magic items and determining their action cost

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

Let's begin assuming you are casting off of a "scroll" in the form of a spell-scar. From the SRD:

The magus can use special scar-based tattoos called spell-scars on his skin to cast or prepare spells, much like scrolls. He can cast a spell from a spell-scar exactly like casting from a scroll; the ink and scars vanish when the spell is cast. The magus can also prepare spells from his spell-scars without expending them, similar to a wizard using the Spell Mastery feat.

The magus does not need to be able to see his spell-scar to use it. A magus has room on his skin for 18 total spell levels of spell-scars, which he can create using the rules for scribing scrolls (although they do not require the Scribe Scroll feat).

In this instance the "scroll" should be able to be used with spell-combat as it leaves your hand free for spell combat and it functions as casting a spell (see the sources cited in the question). I would note that while activating a scroll is a standard action, spell combat works with standard action spells (that being the whole point). Further from an RAI perspective it would be odd for this arcana (being a class feature of the magus) to not function with the primary feature of magi (Spell Combat).

Now let's assume that you are using a more traditional scroll and you can draw it as a swift action via some method (spring-loaded sheaths, being a tiefling, etc) or already have it drawn (because you theoretically could I suppose). Your hand is not precisely "free" but I would argue you can use spell combat anyway because of the existence of the Wand Wielder arcana which reads:

The magus can activate a wand or staff in place of casting a spell when using spell combat.

Two items of note:

• An interpretation of the word "free" in several other answers implies the hand must be empty as opposed to free to cast the spell. This interpretation would render Wand Wielder useless as an arcana and so we can assume that "free to cast the spell" is the correct interpretation, in which case casting off of a scroll should still be fine.
• There is no Scroll Wielder arcana. This is purely an RAI argument but one would assume there would be a Scroll Wielder arcana if scrolls didn't already work with spell combat.

tl;dr You should be able to cast from a scroll using spell combat assuming you didn't need to use a move action to draw it and that the spell is on your magus spell list.