Don't use oil paint to prime EZSand. It's not likely to soak in well, which is the whole point of primer. It will also probably "raise the grain" of drywall, which is hard to fix.
Flat walls with latex paint and patches: Spot prime the patches with wall paint before you start. Or just do two coats, which you'll probably have to do anyway. I use a latex primer when I do a large area or have drywall to paint, but for small areas adhesion not a problem. Water-base paint soaks in.
Washing: I always wipe down woodwork with mild TSP solution in very hot water. It sounds like you're talking about washing the walls. I never do that unless they're clearly sooty, greasy, etc. Latex/ acrylic paint is porous and sticks well, and people don't tend to put their hands on walls a lot, so there's no problem with adhesion there.
Kilz isn't too bad for wood priming, but you'd be better off to use a real wood primer. Simply put, quick-dry primers are handy but they don't soak in well. They're OK for spackle spots and small areas, but not so good for new wood. I like to use Benjamin Moore oil-base primer and underbody paint. It provides a nice base without raising the grain.
If you want the trim to look really nice I'd go with the emulsified oil paint: Benjamin Moore Advance is one. Sherwin Williams makes a better version called ProClassic Acrylic Alkyd. It cleans up with water but settles smooth like good oil paint. The only drawback is that it's a little bit trickier to work with than plain acrylic paint and it goes on thin. You'll need two coats over underbody; probably three coats over regular oil primer. (The BM Advance doesn't clean up as well and the coverage isn't quite as good as the SW ProClassic.)
Regular latex paints aren't bad these days for trim. They settle much better than they used to. But you can never get the same elegant sheen that oil paint offers. Acrylic/alkyd is a compromise between them. (I'm still using Pratt and Lambert Red Seal satin oil when I can get it, but where I live P&L is now gone and Red Seal can only be sold in quarts due to EPA regulations. Last summer I had a big job where I was painting 5 or 6 rooms and had a chance to try out different options, since it looks like I'll have to give up on oil paint soon. That's how I ended up with the ProClassic.)
I've only used Behr once, on a wall. It was surprisingly glossy, sticky and even tended to sag, which is unusual with water-base paint. The result was OK and covered pretty well, but personally I would never use a product like that. It's worth a few extra dollars to buy good paint. Expensive doesn't always mean good, but cheap is very unlikely to mean good. Behr is a HD brand. I don't know what's in it, but even if it seems to be good I wouldn't want to trust it in the long run.
Benjamin Moore is not what it used to be since Berkshire Hathaway took it over and the EPA got in on the action, but it's not bad. Just avoid the watery, overpriced Aura line. The Regal line is good. The newer Regal Select line is OK. Sherwin Williams is good. Pratt and Lambert is very good, but SW bought them, so it may be disappearing. Other brands may be regional and there's been a lot of consolidation in recent years, so I'm not sure what other options you might have.
Also- i an priming the wood trim- I am using Kilz Complete oil based, and then latex semi gloss. I have read that sanding/deglossing is not necessary since the paint there now is flat. Opinions? Is it normal for primer on wood to be able to be scraped off? Thanks.