HOA can be brutal. Yes, you'll have to pull up the grass by the roots - over and over and over again - to control it. For now, spade up the area and pull out the roots as much as you can. If you get it all up to your satisfaction, lay down several layers of black plastic/landscape cloth. Cover with mulch so it looks pretty for HOA. In the summer, when the grass is actively growing, spray it with Round-up (DON'T let any of the Round-up get on the stuff you want to keep). The grass will turn brown and die in a few days. Keep digging it up, Round-upping break-throughs. After a few seasons, the hedges will grow larger, the errant blades of grass will be less, and 6" of mulch will be enough. (very pretty house, BTW)

Hard to tell as I'm using my phone to browse the net but it looks to be either an ash (Fraxinus) or an Elder (Sambucus). The ash will make a very large shade tree eventually and the elder is a white flowering shrub about 10-20 feet high with smelly leaves(not to be confused with Box Elder which is a maple)

My guess is Peruvian Daffodil, sometimes called Spider Lily. Gorgeous plant. I grow them in huge pots and winter them over in the heated garage. They are usually white, but this year I found some in pale yellow (called Sulphur). Two and half to three feet tall is normal I believe, though mine grow closer to 4'. Can't remember how to post pics here and am on my way out the door but if you search Peruvian Daffodil or Spider Lily, you'll get pics.

I don't know what it is but I'm reasonably sure it's a weed. I find them growing in my yard sometimes as well. It's very unlikely that it's a wildflower.