I cannot reproduce any of these, though I haven't tried to block any senders.
I've never seen messages not show up in a search or in all mail. It doesn't search spam or trash by default, but you can override that by adding e.g. "in:trash" if for some reason you needed to include those. It shows me the sender email address just fine when I tap on the header. It also marks a message as read immediately on opening it. I don't see an option to change this on Android, maybe it's a per-account setting you can change from desktop.
when was the last time you used it on Android, and was it on a modern device? about half of those don't really apply/happen to me
1: yeah search sucks sometimes, wish they'd fix it.
2: you can block people, you just have to select the lower ... icon
3: it says 'primary mail' for me, but it is kinda annoying sometimes
4: are you talking about how it shortens 'Steam@steampowered.com' to just 'Steam'? because on a phone there isn't much horizontal room and they have a verified system for businesses but I can kinda see what you mean
5: It marked read nearly instantly for me. If it can load the text then it'll mark as read which only takes like half a second for me.