I actually really like what you've got down already, but I do have some questions.

I take it the PCs are to be humans, or are aliens an option? I'd sooner play a human myself, but diversity among the crew would certainly be interesting.

The paranormal abilities are also interesting- are they to be universal across the PCs, or will only some characters possess them? And how would ESP, particularly its precognitive aspect, function? Would the character using such an ability have to concentrate in some way, or is it more of a passive awareness?

And one last question (or a few related ones), how does FTL work in this setting? You mentioned hyperdrives in the OP, I think- so the ship would pop into another dimension to bypass Einsteinian physics, then? That's a perfectly reasonable way to go, but how long does it take to get from point-A to point-B? Say, for the sake of argument, how long would a Sol to Alpha Centauri (about 4.4 light years) take? Is it instantaneous, or does it take a bit?

I hope I'm not coming across as demanding, but I'm just curious.