You can't prevent many of these. They're a major part of the genre. Taking them in turn...
1 Using the Transporter to Save the Day
You need to clearly define your allowed limit on transporters. "Decanonize" certain episodes to prevent "repaterning" people. But, once those limits are set, further nerfing simply makes you a bad GM, and is not indicative of bad roleplay.
I run trek with a pre-pattern-buffer timeframe and a "No messing with the matter within" caveat. It's not that I won't have malfunctions happen - I simply won't let players replicate them.
Set your limits clearly. The shows don't, but don't need to; Gaming does need them set. Pick them, stick to them, and accept that within those limits, you as GM need to suck it up.
Simply enough — restrict to yes/no/maybe answers, or "which of the given methods works best" type questions, and "how long" type questions. And accept that general reference data and probability matrices are areas where they should be using the computer, and they should get valid answers out.
Nerf the computer too much, you lose the trek feel.
4 Brilliance Out of the Blue
If it's a good idea, it's a good idea. It's best to let them run with it.
You may need to have the appropriate character be blamed for it within the context of the fiction — not every brilliant idea put forward by the Doctor's player is suitable for the Doctor to think of, but if it is an engineering solution, and the Engineer's player thinks its the solution, then simply have the two play out the discussion where the Doctor and the Engineer come up with it together.
But also, keep in mind that, in theory, most PC's in Starfleet should be amongst the top 1% intellectually (and those are the dumb ones, Starfleet's top 1% are the IQ 200+ crowd), and many have extensive cross training. So, the "shouldn't be thinking of that" bar is pretty hard to cross, anyway.
5 Special Racial Powers
Stick to what's been established. If they come up with novel uses for those powers, great. LET THEM No "new powers" just new uses.
And make certain to note these new uses for future reference.
6 Time Travel
Is usually imposed by the GM. Just simply state ahead of time that you don't allow it. If they try it, kill them. "...harmonic reality vibration shatters the warp core - KABOOM!!!"