Yep, ragweed, pull it now before it flowers and makes more for next year.

I agree with NHBabs. The red-stemmed plants look like a dewberry (Rubus) species. Those have canes that are arching to prostrate, with whip-like tips that can root when contacting the ground. Inflorescences are usually found in the middle third of the canes, with flowers expected Apr-May.

I didn't want to mention the rock slide that crashed through the wall if it wasn't already bothering the homeowner's. Sometimes people don't want to have their attention drawn to something that's expensive to fix, if they're otherwise accepting of it. Since it came up, I'll not disagree with kiminpl's comments about the two elements being radically out of sync. I think the problem lies entirely with the rock fountain. We notice that the rocks are of relatively uniform, small size. In nature we would see some boulders in the mix. Also, the chute is straight, like a manufactured object. At the termination point, the stacking of stones is not at all like nature would do it, stable and in equilibrium. Instead, some stones are stacked vertically so an accidental bump could send them tumbling. That the "stream" has a given width at its base, but where it penetrates the wall it is only half that width, which looks unnatural. The pool at the base should be wider -- probably considerably wider -- than the stream, if it is to look natural. And It seems that replicating/simulating nature is the whole point. Looking at an example of a natural stream (or a good fake stream!) a quasi-alternating arrangement of boulders occurs more or less along the sides (encircled in yellow.) The boulders are "helped" by large, dome-shaped plant masses (encircled in orange) furthering the random, alternating arrangement. One might think of their arrangement as how a steel ball might travel a pinball course (red line.) In some cases these boulders extend, separate and outside of the stream, adding depth and drama to the scene. In the case of the property in question, no boulders to speak of exist at all! I would be tempted to mortar some stones together, making simulated boulders. (To be sure, though, it would require someone with an artistic sense to do this and massage the existing contents into a more natural arrangement.) Consolidating stones into larger masses could help to create more of a meandering effect. (It looks like the actual path of water flow might be curved.) It could also help to narrow the overall stream so that it fits better with the wall opening. It's going to be nearly impossible for me to describe in a concise way how the stream should meet the wall, but I think this portion needs a complete redesign. While the largest "boulders" might begin to penetrate the wall, I don't think all the "gravel" looks good spilling out and filling the pool. It should be more pool and less stream bed on the patio side of the wall. Given that the "pool" probably needs to be filled with gravel, it might be a smaller, different colored (dark) stone that simulates the effect of water. Don't know if this will help. Usually, creating these things like this are not for people working it out as they go. It generally takes someone with experience.

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.