Can you please tell me what defence dice the familiar uses?
None, initially. There's a Necromancer skill that grants him a brown die.
Can the familiar remain in play until it is defeated?
Yes. It can also be dismissed at will during the Necromancer's turn, if he so desires.
At first glance this seems very strong for just the use of one fatigue point!
Is this to make up the fact that the reapers scythe is a weaker starting weapon?
More like the scythe is a weak weapon to make up for the Reanimate being so powerful. Familiars in general are a fairly potent addition for any hero, as they often grant extra actions during a turn and actions are the most valuable things heroes have.
That said, though the reanimate is definitely useful to the heroes it's also very easy to kill. A good OL will have the Necromancer spending that fatigue (and action) nearly every turn in order to keep the reanimate on the board.