Thai is done on a mat on the floor fully clothed.  It is about grounding and opening the body up.  There is more passive movement involved in Thai massage that you would not be able to receive from being un-clothed under a drape on a table.

No, I did not study that type of Thai massage (were the practitioner uses a bar to support their full weight on someone).  I studied in Chaing Mai (northern Thailand) and use my feet in slow deep manner on many parts of the body, but not to walk on someone’s back.

That is completely up to you.  In the winter months, when it is colder, it might be nice to keep them on to keep the feet warm.  I have worked with both socks on and off.

That very much depends on what you are looking for.  I would say that if you want to receive a Thai massage and really get an idea of what it is, book 90 min.  I do realize people have time and financial constrictions, so I do offer a 60 min Thai session but it will seem really fast.  If you are looking for something more specific on just a certain area of the body book 60 min (this applies to all modalities).  Of course, if you want specific work and full body a 120 min might be what you are looking for!