2 months after bilateral laparoscopic inguinal hernia surgery, my right testicle hangs higher than left, and spermatic cord is still sore, normal?

Yes. What you describe is not unusual. It is normal for one testis to hang a bit lower than its mate. You are likely the same as you were prior to surgery, but now you are focused and more aware of your anatomy. The cord tenderness will be resolving soon.
Absolutely. Changes in the way the testicles "hang" is completely normal - whether open or lap surgery. Always interesting how the same thing is done on both sides but the two don't act the same!