1) Yes - the form has a line for New Agency Name and New Travel Advisor's Name (if applicable). You need to contact your TA (or agency) and have them send you the request form, all their information will be already included.
2) If you find a fare drop or better deal, your agency can either apply it for you or re-book it.
3) I don't think it matters if your agency does not show the stateroom as available -- of course, if you already booked it with Princess, it wouldn't.
4) From the form: "Bookings may only be transferred within 60 days of booking creation so long as (a) the request is made outside the Final Pyment period, and (b) the booking is not paid in full." I don't anything regarding sales, maybe someone else has more info.