1. All the balls are needed
2. I'm not sure you can with the blue ball, but it's possible with the purple one :a2:
1. All the balls are needed
That's not true, actually. By corner glitching you can skip many of them. If I am not mistaken, it is possible to beat the game without balls 2, 4, 6 and 8.
You start with :a1:, with which you enter the tower and get :a3:. Using that, you can get :a5:. With corner glitch you can use that one to get :a9: (which leads you to :a0:) and :a7: (needed to enter the lab). These are also enough to input the final code in the lab.
Yes, the glass ball can go in there. It's hard. You need to get blown up from the lava pit to the right and manage to that entrance.
Or you could use the corner glitch to get into shadowlands, get the frozen ball, go to the future and get the flying ball, and use the flying ball to get into Crystal Path.