When I'm playing Wing Commander 3, the ships seem to be really difficult to maneuver. I'm using a keyboard, and it's very difficult to turn quickly. It seems to be harder in some directions than in others; for instance, moving down seems to take longer than moving up.

Has anyone else had a problem like this? I feel like I'm flying in molasses.

If you are using a keyboard, hold down the shift key while you are maneuvering. It greatly increases the speed.

I have a problem in the mission with the "skipper" missile. I'm using the ship, that can carry a torpedo, in order to quickly kill the enemy corvette.

However, I often have to repeatedly press shift, rather than hold it down, in order to turn more quickly. Which is extremely annoying in itself.

Furthermore I've experienced a few times, that I suddenly am unable to to up at all - this has happened twice when I jump to the location with the corvette.

Other than that I really like the game, but I'm seriously considering dropping the game. Buggy controls can really kill the enjoyment with a game.

Try playing with a joystick or an analog gamepad, if you haven't got those try the mouse controls.
Wing Commander 3 wasn't designed with keyboard controls in mind I'm afraid.

No kidding... I tried the mission again, had the same bug. Gave up on that ship and tried with one of the faster fighters. Managed to shoot the skipper missile and wreck the kilrathi ships. Sweet, mission accomplished I thought. Except not. Now the controls bugged out in a new, exciting way.
I could no longer adjust the velocity of my ship. I could only switch between maximum normal velocity and starting/stopping thrusters. Nor could I auto-pilot. Not that it would have helped, since I couldn't stop and land to end the mission.

I might some day look at setting up my 360-pad, but I have very bad experience with mousecontrols for space shooter games.

The keyboard controls were perfectly fine for me in Wing Commander 4, so I'm pretty disappointed the predecessor is so much more buggy (for me). Earlier game, I know, but still.

Did you try using the Win 95 KS patch in another thread?

That should help a lot.