Technically yes - either from a PC or from its crew rating if an NPC vessel.
Not sure what happens if no PC is on the ship - I'd guess crew support is needed?
Also remember that many situations don't require a roll.
As an aside, this is one of the few flaws in the system for me. Outside of the talents and the like, there's very little difference between vessels statistically, as crew rating is more dominant on any task rolls.
No. Any assist is rolled regardless of the result of the Task Leader. If the Task Leader generates at least 1 success, then any successes from the assist are added. However if the Task leader fails then the assist cannot add successes, BUT it can still generate complications!
I always ask the Ship assistance and Character assistance rolls be done before the primary lead does their roll. That simulates them putting the work in, but the ultimate success depends on the final roll by the Lead. And the complications from assistance are thus taken into account.