Try to think of all the possible ways landscapes can be useful: provide light or shade for various related purposes; provide spaces to entertain, lounge or for recreational activities; provide beautiful views; screen unattractive views; a place for pets; places for storage & utility; etc., etc. Do you need any of those things? Designing a landscape is assessing all the needs and finding (as much as possible) ways of fitting them in or accomplishing them.

Just get straight glyphosate - it doesn't have to be RoundUp specifically and there are less expensive brands of this herbicide on the market (Ferti-lome sells a product called Killzall that is less than half the price of the equivalent concentration and size of RoundUp). If you do go with the RoundUp, just select the Weed and Grass Killer - no need for any other additions to the mix. As I noted previously, you may very well need several applications and it is suggested to allow at least 2 weeks after the last treatment before reseeding. And it is too early to reseed - too hot and too dry for most northern, cool season grasses to germinate well. Generally, the ideal time for fall seeding is early fall - September to early October, depending on your specific climate. And any cool season turf grass blend recommended for your area is fine. Most independent garden centers - not the box stores - will have blends that are appropriate for your area.

If you want a retaining wall, hire a designer who is qualified to do so. In many municipalities, retaining walls above a certain height require engineered drawings and planning approval. There are also drainage issues to consider which may be beyond a homeowner's purview. The easiest course of action would be to replant the slope with a groundcover that will prevent further erosion and provide an attractive green backdrop. But you will need to keep the dogs away/off until it becomes fully established.

It's always hard to get a read on slopes from just pictures, but here it seems pretty obvious. The water is flowing along both sides of your house to the back corner of your property, and carrying down between the neighbors to the lower street elevation in front of their houses. You just need to form your grade to allow that to continue as it wants to go naturally. As far as your patio, it is lower than the grade. You need to dig down the adjacent area next to the plastic edging, under the trampoline, and probably remove the buried concrete "curb." Slope however needed alongside the wall of house towards the corner instead of towards under the trampoline. It would be good to do a test dig behind one of the concrete walls to see if there is a drain tile at the bottom, I'm guessing there is not. A french drain in RED would need to be at the bottom of the wall and run to daylight. Create a small swale in GREEN and direction of water in BLUE. Verify your neighbor's in PURPLE is not coming in to your yard.