You can wear whatever is comfortable for you.
During certain types of massage you can such as Thai massage, Shiatsu or chair massage.
Depends where you go it's more likely not to be but check when you get there personally I think No
You leave your underwear on.
You are expected to leave on underwear (as in underpants) during a massage. Trained therapists will drape you with the sheet/blanket so that only the part of your body being massaged is exposed.
DICK?
You leave your underwear on during massage. When I've had a massage I've always been naked.
Shorter clothes
Yes, you are allowed to wear whatever makes you the most comfortable. There are massage styles where the recipient remains fully clothed the entire time.
If you are modeling for a clothing company then yes, you will be wearing the company's clothes during the shoot. Usually you are not allowed to keep the clothes afterwards, however.
Hercules was a demigod stuck on Earth. He is always portrayed as wearing the same clothes because those were the clothes worn during that time.
When you get a massage of any kind, it is not necessary to be disrobed of all your clothing. Not even a French massage. Some modalities are performed more easily if the cloths are removed, but this is not a requirement and no professional massage therapist will ever force their client to do something they are not comfortable doing, even removing clothing.
Yes, it is common to become aroused during a massage. A massage provides stimulation, and stimulation can be arousing.