Excellent, ICOT and RONSR.
As far as plungers go, the black ones with big double-layered tapered sides are much more effective than the flimsy red flat-ended ones. Having some water in the tank makes plunger work more effectively, as it fills with water, not air, which works better, as you mention. So if water level is very low, then sometimes pays to flush ONCE before plunging. However, if water level is high already, or if you flush twice, you will overflow sides of tank and have a much bigger mess to deal with. It is a carefull judgement call.
Now on the subject of showers, can those new types of single knob shower controls be fixed when they begin to wear out without breaking all the tiles and requiring a very expensive rebuilding of a shower? With a regular faucet, sometimes all you need is to replace a rubber washer. However, can similar maintenance be done with these fancy shower fixtures? It would be a poor design if you need to replace entire shower for a simple repair, but at least one person told us we may need to do so.
Another question: In a basement where the main drain is above floor level, in order to install a bathroom we have heard it will require special pump. Are there reliable? What happens if power goes out, will we have a major mess? What about using on Shabbos?