This is not what you want to hear, but get used to it. It happens and will continue to happen. If your corals are humming and looking great, nobody will even notice.
Yes, but with variable results. It depends quite a bit on the depth of the scratch. I've read about two methods:
filling with super glue
cerium oxide and buffer to buff out the scratches
I can only speak to the results of using cerium oxide, as that is what I tried. It worked for small scratches really well. The deep scratches it did help, but I didn't get them out. I have some pics of the process I went through on my build thread.
It does make quite a mess... I'd recommend doing it outside. FWIW, I agree with @jda. As much as I hate the scratches too... after going through taking down the tank to try getting them out... I don't know that I would say it was worth it... it's almost inevitable that you will get another one, two, or three. For me, my latest ones are from well intended tank sitters that cleaned the glass with magnetic scrubber too low to the sand bed.
I think of it as dents in a new-to-you car... the first few are so aggrivating. Eventually... you stop noticing them.