Yea, I've heard all those rules about flat tops too and when I first bought this house 10 years ago I was worried because of that. That said, I use cast iron exclusively and my kids cook daily on the stove top with cast iron as well and we've never had an issue. I only point out that my kids do it too to prove that, in least in our case, it doesn't require precision and extreme caution because my kids are good at neither.
I also can on my flat top and have never had a problem. I've never used a stove top pressure cooker on it only because i haven't used a stove top pressure cooker since owning this home.
My fave cleaner for my stovetop is "Bar Keeper Friend." But for the most part unless I have something cooked on that I need to scrub off I tend to just use whatever basic spray cleaner I'm using on the rest of my kitchen.