Is it necessary to remove scotch tape off walls before repainting?

Yes, the paint won't stick to the tape and even if it did, you would be able to see the outline of the tape afterwards. It will look much neater if you remove it first. Preparation is 9/10th of the job!

Yes. Otherwise you run the risk of paint not sticking to it. Also if it comes off after you've painted then you'll have the old colour showing through. Plus it just looks bad if you don't because it can show through your new paint.

Yes, plus any residue from the glue on the back of the tape that remains on the wall.

Definitely!!