If a Necromancer spends an action to summon his reanimate. Can he activate the Reanimate in that same turn? As in, once he finishes his other actions?

Yes, the Reanimate can be activated that turn, but only after the necromancer has finished its own activation.

Can the Reanimate move? has it got two actions but with only one attack or is it only able to attack?

The reanimate has the ability to move and to attack (once each) every time it activates.

Than ks