Answering your questions one at a time.  You could still transplant your tomatoes to a clay pot but you should have someone help you.  Water the soil extremely well.  This way it should stick to the roots.  With someone helping to support the plant, tip it to the side and, with a plastic underneath, slide it out of the pot.  Then using the plastic tarp, lift it and gently place it in the new pot.  Tap it down and maybe add a little more soil.  FYI if you purchase a bigger plastic pot in the future you can put rocks or something similar on the bottom to weigh it down.    It is probably too late to put a tomato cage on your plants now but next spring it is good to put them in the pot when you plant your tomatoes.  Then put a stake in the center.  You really should use ties that have a lot of give.  Consider purchasing a cheap package of knee high women's nylons and cutting them across the leg, like a ring.  Clip that ring and use the result to tie your tomato to the stake.  If you tie it in a bow, the ties are re-useable.  I just picked my first 6 cherry tomatoes from a pot on my deck Saturday.  Soooo good.