Generally you are nude, but you can wear underwear, especially for women who are menstruating.
During certain types of massage you can such as Thai massage, Shiatsu or chair massage.
DICK?
It depends who's massaging you - I imagine it'd be easier without clothes, but I doubt anybody's going to force you to strip...
You wrap yourself in a towel.
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.
You can wear whatever is comfortable for you.
Generally you are nude, but you can wear underwear, especially for women who are menstruating.
Sure. There is no problem leaving your underwear during a massage.
Yes, it is common to become aroused during a massage. A massage provides stimulation, and stimulation can be arousing.
Yes you can wear cloths during a massage. In most all Asian bodywork therapies, like Thai massage, Acupressure, or Shiatsu, the client is fully clothed throughout the massage treatment. Also, for Western modalities, if you are having a massage for the first time, your therapist will be very understanding if you wish to keep some, or all of your clothing on. On a final note: You are never NUDE, at any time, during a massage treatment. You are always covered with a drape. And. only one part of the body at a time is uncovered. By-the-way, this process of keeping the body covered and uncovering the parts getting massaged is called draping. Draping means the use of a drape, it has nothing to do with whether something is covered or not. It is the system, process, and procedure of making a professional statement about the level of formality in the client/therapist relationship.
Many massage parlors offer a variety of services during a massage, such as a Swedish massage, a hot stone massage, and prenatal massages. During the massage itself, many parlors use relaxing music, soothing body lotions, and hot towels to relax the customer.
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.