I thought that the hardiness and drought tolerance were unusual. Like I said, the other three roses on the property were nearly dead (very few leaves, those left were diseased, no blooms, etc.) but this one was healthy and blooming without any supplemental water and in part shade. If you can't identify it, then suggestions for roses that are as tough and continuous blooming would be appreciated.

The last one looks like it is a sweet rocket or hesperis matronis. It's a reasonably tall lavender coloured flower that blooms over a long period. They self seed, but are very easy to pull out and as they tend to bloom a long time in my garden I always welcome some in my garden.

Looks like a papaya ....

I think your weed/vine might be one of the small flowered clematises like sweet autumn clematis or clematis virginiana, which has several common names. In order to identify it for sure, you can let it grow out and bloom. You might find it to be something that you even like. I have a number of species clematises that reseed with abandon. If you really want to be rid of it though, be sure you are digging out the roots. You can also post on the Name That Plant forum where lots of expert plant identifiers hang out. Good luck, spiderwoman