One object, creature, or spell is the target of the dispel magic spell. You make a dispel check (1d20 + your caster level, maximum +10) against the spell or against each ongoing spell currently in effect on the object or creature. The DC for this dispel check is 11 + the spell’s caster level. If you succeed on a particular check, that spell is dispelled; if you fail, that spell remains in effect.
When you target a single creature or object with multiple spell effects, you get to roll once against each effect, potentially dispelling all of them.
The wand of mirror image applies a spell effect on the creature, so it is included. But as for the ring of water walk and ring of protection:
If the object that you target is a magic item, you make a dispel check against the item’s caster level. If you succeed, all the item’s magical properties are suppressed for 1d4 rounds, after which the item recovers on its own. A suppressed item becomes nonmagical for the duration of the effect. An interdimensional interface (such as a bag of holding) is temporarily closed. A magic item’s physical properties are unchanged: A suppressed magic sword is still a sword (a masterwork sword, in fact). Artifacts and deities are unaffected by mortal magic such as this.
So you have to target the ring of protection or ring of waterwalk specifically to dispel it, and dispelling it only suppresses it for 1d4 rounds. Targeting the person wearing the rings doesn’t dispel the rings.
When dispel magic is used in this way, the spell affects everything within a 20-foot radius.
For each creature within the area that is the subject of one or more spells, you make a dispel check against the spell with the highest caster level. If that check fails, you make dispel checks against progressively weaker spells until you dispel one spell (which discharges the dispel magic spell so far as that target is concerned) or until you fail all your checks. The creature’s magic items are not affected.
When you target an area, you only remove one effect from each creature. The effect removed is the one with the highest CL that you manage to beat. Magic items are not even considered for this form, but the effect of the wand of mirror image is.