Chrissy -
Clematis are perennial and prefer rich loose soil (no root competition), full sun with regular water and mulch or shaded feet. If they are in a spot where the soil gets hot, they are doomed. They climb, so they need some kind of support, and you may have to 'encourage' them to go where you want. The common large flowered varieties can be susceptible to clematis wilt which results in blackening of the vines and leaves. Do not replant in the same spot if you replace one with this disease.
Thunbergia depends on the variety I believe. All will be annuals where you are. The 'black eyed susan' vine should work well where you have it, assuming you can keep those pots watered and they are in full sun. The large blue flowered variety is more of a climber (IMO).
I have grown Moonvine more than once without success. They grow for me, but I rarely got flowers on them. Not sure if my soil was too rich, or what, but I can't really help you with those as I gave up on trying to grow them!
Good luck,
Jennifer
