Paulownia tomentosa

I'd say Yucca flaccida, rather than Y. filamentosa. The latter has stiff leaves, while the other one is, well....flaccid!

Likely, Gaura lindheimeri 'Siskiyou Pink'

I'm in Ca. each house is a little lower or higher than last house. Stair-Step style I guess you could call it. They want you to think you live on a slight hill. Anyway a neighbor's water could run onto our property so we put a drain pipe out to the street along side the house buried with a small grate at each end that's cemented around outside of pipe to carry water out of back yard & out to street. We don't get much rain here but did see about 6 inches of water round in back once long ago & most drains off. I don't see any reason you would be going onto his property. We have common walls here too, we each paid 1/2 of block wall & it's on the property line, usually there is at least 5 ft beside the house, maybe you need to put more dirt in so check with inspector to see if your property was properly graded. Our new home was a shock because day we signed the papers we came over & they had graded the back yard, high way at back & all water would run into house in storms as large patio door, sliding glass, only few inches above dirt, lucky for us they came & regraded it but we also had to do a lot more work & make it so we wouldn't have problems. I think problem is with your place not being graded properly. Guy that graded it probably didn't know a thing about grading, just thought you move some dirt around so looks ready to plant.