I really want to participate in a certain program; can the trainer accommodate me if I don't have access to all the equipment or if I follow a special diet?

In most cases, yes; the trainers are able to create an eating plan and nutritional guidelines based on most any dietary needs. Some trainers can adapt a program for bodyweight, substitute exercises for equivalents, or work with constraints from previous injuries that prevent doing certain movements.

If you have any questions, you can contact the trainer directly from their team fitness page.
Select the program that you are interested in. On the left hand margin of each program page, there is a link to the trainer's Fitocracy profile as well as any other sites through which they can be contacted. There is also a blue button marked Questions? which allows you to email the trainer.