I've done BJJ, Kick Boxing and Karate when I was younger.
But it was when I was pre-t and nothing was changed.
I stopped because of transition but here's my advice.
Everywhere I've done mixed martial arts, very few people took their showers at the gym.
Most just took our gi off and left.
When it comes to locker rooms, no reason for anyone to see your junk.
Just come to the gym with shorts and a t-shirt, and throw your gi on top once you get to the gym.
Most guys don't wear a shirt under the gi though, but I doubt anyone will question you about your scars.
Btw your gi WILL come off eventually in a fight. So if you don't want people to see chest scars, keep your tshirt under.
Also make sure your shorts under your gi are well secured. I'm sure you can guess why.
Third, guys wear jockstraps (duh). So as long as you have one on, no one will question what's inside the cup.
Personally, I wouldn't put a packer in there because fighting bjj can get crazy, you'll be rubbing and twisting
all over your partner so the chances of a packer sliding out would be very high.
Your call.
Hope that helps!