Yes, the start is tricky, but once you absorb one sun, it gets easier.
So you have multiple monitors and the mouse moves away? I locked and hidden the cursor, if you start the game in main menu, so that would be a strange behaviour you encountered. Moreover, I can't really test it, because I have only one monitor.
The "black" you experiences is probably the void. Not all the space is filled with stars and you can look in directions where absolutely nothing is.