hey,
so ive never worked with lwjgl but i just looked at the docs in order to try to help you and i have to say i reallllyyy dont like it.
Also sadly your code aint really commented at all so i had some trouble, but i think i might understand most of it now.
anyways,
Issue 1: i kinda find it strange to let the level move how you do it(if ive seen that right). but i suppose you could change the speed ?
or if this doesnt work you could :
Game.level.xoffset -= (int) x * 0,5;
Game.level.yoffset -= (int) y * 0,5;
Issue 3: now in order to that i would add debug lines here :
if(keyboard.pressedKeys.contains((Integer) Keyboard.KEY_W) && keyboard.pressedKeys.contains((Integer) Keyboard.KEY_A)){
System.out.println("[Keyboard] W + A pressed - this works");
this.playerMove(-speed * Math.sqrt(0.5), speed * Math.sqrt(0.5));
return;
}
and in the checks for the other keychecks.
Also i would add something like :
public void playerMove(double x, double y){
System.out.println("[PlayerMove] - X : " + x + " - Y : " y );
Game.level.xoffset -= (int) x;
Game.level.yoffset -= (int) y;
}
maybe this way you can see the problem.
Issue 2 :
cant suggest much there, i just found this:
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, <texture shrinkage filter>);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, <texture expansion filter>);
which maybe will let you expand or shrink your stuff 
