[RPG] Can a Cleric use a magic item that casts Wizard spells

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:

Spells of the prohibited school or schools are not available to the wizard, and she can’t even cast such spells from scrolls or fire them from wands. (PHB1 p57)

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.

That depends on if it is casting a spell, or granting a spell-like-effect.

To cast an actual spell from an item, it requires your concentration. This is specified on page 141 of the DMG

[...] The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration.

This rule would be used in the case of an item such as a Staff of Fire, which allows you to use it to cast the spell Wall of Fire (which requires concentration).

However, to cite the specific example you gave of a Ring of Invisibility. No.

Again, per the DMG, page 141...

Many items, such as potions, bypass the casting of a spell and confer the spell's effects.

The rule for concentration applies if the magic item allows you to cast a spell. It does not apply if the magic item grants you a spell-like effect. The stats on a Ring of Invisibility say

While wearing this ring, you can turn invisible as an action.

It does not say you can cast the spell Invisibility...just that you may turn Invisible as an action. This is an important distinction.

Thus, a Ring of Invisibility does NOT consume your concentration as it grants a spell-like effect, rather than allowing you to cast a spell. A Ring of Water Walking is another example of this, in that it allows you to walk on water at-will, rather than allowing you to cast the spell Water Walking.