1) Quite often I can't select anything. My cursos reads "Left-Shift" and as soon as I press Left Shift, it's fixed. But it's quite annoying having to press Left Shift so often, so how do I prevent this from happening?
The only way to completely prevent it is to never, ever tab out of the game or bring up the Steam overlay or do anything else that removes focus from the game, pretty much. It's a "feature" of the Unity engine the game is built on. Several other game engines I've run into, too, actually, but most of them don't let you know they think the key's stuck after entering/exiting the Steam overlay.
2) During the campaign tutorial, I'm at the part where I need to raid (destroy) a warp gate. I got two human raid starships and a transport ship but I can't figure out how to actually destroy them. Is there some kind of building that I need to destroy? I tried the Wiki and Google but couldn't find the answer.
The warp gate is a structure in the enemy system that you need to destroy, generally next to their command station. Zoomed out, the icon is small and kind of boxy, while zoomed in the graphic is sort of a long bar with rounded ends, like an Arkanoid paddle.
Oh and one more thing. My resources are usually maxed but I don't really know what to do with all those resources. I already have a main fleet of 500 ships and plenty of turrets. So, any idea's?
If you're just doing the tutorial, it's not going to be a terribly high difficulty, so you're not going to be playing very aggressively or getting attacked much, so you're not going to be losing many ships and needing to replace them. In a real game, the solution to having too many resources is to go pick a fight (not just for no reason, but go after your next target, since you're in good shape to do it), or wait a few minutes and the AI will come start one for you, especially later in the game or on higher difficulties. The harder you set the AI and other game options to be, the less you will have to worry about having too many resources. There are a whole lot of ways to use them up in a hurry when you're not in "it's the tutorial so there's limited challenge" mode. Heh.