Hi harry,
Passionflower and mandevilla, can be rooted from cuttings. I have rooted mandevillea by layering. I will post a link on passiflora propagation. Sweet potato vine roots easily in water of soil. Not sure about wild basil but regular basil roots quite easily.

Here is a link that might be useful: passiflora cuttings

Depends a little on what kind of begonia you're growing how to propagate, but begonias in general are pretty easy usually. Techniques vary according to type. I haven't tried Magilla perilla, but have a friend who turned one small cutting into dozens of gallon or more pots over the winter--she loves to propagate and has a lot of experience, but I think she just stuck it in a pot of good potting mix and then took more cuttings as the first one grew. They're gorgeous!
There are several different vines that are known as potato vines. Are yours Solanum? I haven't tried them but I don't think they're hard--just be sure with all your cuttings to use a good-quality potting mix and keep them moist but not soggy. As you do more of them you'll get a feel for what works for you, which might be different from what works for someone else. Cuttings are usually pretty easy as long as you don't forget to water (one of my failings!)

Magilla Parilla is really easy, I bet it would even root in water. Can't say on the others as I haven't tried.

GOOD LUCK!

Magilla Perilla is easy. During this summer when I pinched out the top so it would branch, I pinched out two nodes and just stuck the broken off part in dirt. It rooted... Also, I've got some right now in a glass and they have roots. I plan to put them in dirt and overwinter them.

The crepe myrtle can be rooted in the same way. Just make sure you have some of the 'hardened' wood. You can scrape it at the bottom, dip in RootTone, and gently place in dirt. It will root easily.

Hope this helps. :)