1 is possible in terms of the several IMAP accounts, and I doubt you'd see any issue with lag from having 10,000 emails (though I wouldn't know exactly, as my largest one is around ~2,000). The application doesn't load them all at once though, so I don't think there'd be any issues with that.
2 is something I do on the daily. I have an appointments calendar, my workout calendar, my school calendar, and a holidays calendar, and they all sync fine.
4 yes, folders are a thing, but I have several thousand pictures, and if I choose to view them all at once, it works flawlessly.
5 is a no, *I think*. I don't use stamina mode, and I get at least 30 hours of battery life with pretty heavy texting regardless, so...
7 yes, and even though you can't fully remove a few applications without root, most all of them can be disabled without root.
8 no, not that I know of. I use both, and they both charge pretty fast.
9 yes, not locked down.
Xperia ion - Retired
Galaxy S4 - Backup phone (slightly cracked screen)
Xperia Z2 - Current phone
Xoom 4G - Retired