I think the first one is a wallflower.

From what I understand, zoysia is just a fancy bermuda grass. goodbye gardens and flower beds! there is a chemical now thats supposed to kill it, but roundup wont touch it. good luck, i've battled bermuda for 40 years--its winning.

How much standing water did you have in your yard? Other than breeding mosquitoes, I wouldn't worry about standing water in my neighbors yard, better theirs than yours . . . however, if you have drainage issues on your property, that's dependent on slope. I can't tell the slope, but from a casual glance, it looks like your yard is the higher ground so drains into theirs. I wouldn't plant a rose garden in an area of standing water. I'd either do a rain garden or a french drain, as some have suggested. Then plant the rose garden outside of that zone. The rain garden and/or french drain will hold and slowly release the water so they will take care of that part, leaving another higher ground area for the roses . . . Roses like moist conditions so if it's just occasionally for a few hours after a rain maybe not a big issue if the roses are the right kind. I love me some "Rosa palustris" which is the native swamp rose, it would do fine there, it is a stunning bloomer but not repeat. But of course roses hate dampness, so if the water is there for any length of time it's not going to work for other roses. Figure out a way to drain it away first, then deal with the roses part . . .

Prariemoon - it was a couple lawn/yard guys who cuts grass and trims hedges. They really cleaned it up and out so I’m half expecting them to return and at least put down mulch in the flower beds or the weeds will be back in no time. There’s now a nice long border to fill - open space that if it were mine to fill i would plant with annabelle or incredibelle hydrangeas. I may offer her some cuttings….