A.) can a reanimate revive someone?
Nope. Familiars only get the Move Action by default (and assuming they have a Speed rating, since a move without a valid Speed wouldn't work very well =P) Other actions are available only if the familiar card (or some related class ability) says they can do it. The Reanimate's familiar card says it may attack once, but no reviving. =)
B.) can a reanimate be a target of the Disciples prayer of healing? Not for the healing effects but to gain the extra attack dice or defense dice (I can't recall the name of the powers that grant the prayer of healing the extra buffs.)
Yes, the Reanimate may be targeted by Prayer of Healing.
The Reanimate is treated like a figure (per its familiar card), and FFG has clarified that any familiars "treated as a figure" may be targeted by attacks, hero abilities (which includes class skills) and overlord cards that target a hero.