Hi!
The area around the Jungfrau is one of my favourites in Switzerland. The two valleys are quite different. The Lauterbrunnen valley is a glacial U-shaped valley, so it can be quite dark unless the sun is overhead. Grindelwald is much more open, though the route up is narrow. There are lots of good walks around both valleys. If you go for the walk along the "base" of the Eiger, the sun is only there in the late afternoon. There are lots of cablecars and railways; its very enjoyable to ride up, and gently walk down. You'll generally find a restaurant for refreshments along the route.The waterfalls generally are at maximum volume when the snow melts, so from around May for a month or two. The train up to the Jungfraujoch is expensive, and it's only worth going when the sky is completely clear -- there's a webcam there, worth checking before you go. (And it's cold up there! And the sun is very strong.) Grindelwald is rather over developed; Mürren and Wengen less so.
Lake Lucerne is a beautiful area; the old town is pleasant, but the bridge over the river is a replacement -- the original burnt down about 10 years ago. You can take a boat trip down the lake and back again, but this does take most of the day; relaxing if you have the time. The Burgenstock is pleasant, and has an amazing outdoor elevator. There's a rack railway to the top of Pilatus, if you have the time.
Zermatt is at the top of the valley; it's "car free", but be careful, as the electric vehicles and taxis are almost silent and are ubiquitous. A classical trip is the railway to the Gornergrat, and then walk down; there are views to the Matterhorn. But as to the best location for the reflected Matterhorn, sorry, I don't know.
Bettermeralp is a pleasant area -- but there are so many pleasant areas. The glaciers are retreating everywhere; if you go to the Marmorbruch in Grindelwald, you can get a very good idea of how things used to be. (The food there is great, and you can (could) stay overnight, though it's a little basic.)
I have been disappointed by the Rhine Falls; you can get to a viewing platform, but somehow, although the falls -- really a rapid -- are impressive, I've never been able to make a decent photo of them. But if you're in the area, and like architecture, go to Stein am Rhine for the oriels and the decoration. (Wangen an der Aare is a similar old world town.)
Q1> It can get hazy in the afternoons; check the time tables on sbb.ch for train details. You can't stay on e.g. the Jungfraujoch overnight any more. I've only ever gone up early in the day.
Q2> There will still be water in the Staubachfälle in July, though probably not the maximum: the Lauterbrunnental is roughly north/south, so light should be best around mid-day (remember that Switzerland in GMT +1; and they have summertime there -- which is GMT +2)
Q3> Sorry, I don't know, but as above, the walk down from the Gornergrat is the "classical" one. (Sadly, there aren't that many walks around Zermatt -- it's more for the skiiers.)
There's almost nowhere in Switzerland which is ugly -- the outskirts of Zurich and Basel are industrial -- so no matter where you go, you will find natural (and artificial) delights. Although it's a small country, there are delights in every valley. You need far more than a week to take it all in; I'd suggest a limited itinerary, say, Jungfrau area, then over the Brunig to Lucerne and environs, rather than attempting it all. Zermatt is pleasant, but the journey there does take some time -- as do all trips into the valleys -- it might be something for next time. If you do go to the Jungfrau area (not that I'm at all biased!), have a look around the old town of Bern; a jewel, a world heritage site, and take a climb to the top of the Munster, and ask the ticket collecter where he lives. Further along, Thun also has a very pleasant old town...you could spend quite some time in both these places...
Enjoy your trip!
