POP3 keeps emails on the server, so a read email is read, but a deleted one is deleted - for all users.
IMAP keeps the emails on the phone, so reading or deleting them does it just on the phone, but not for others.
You can have different accounts set differently in GMail (go to
GMail, the meatball (or gear) icon (upper right), Settings, the Forwarding and POP/IMAP tab to set each account the way you want it). But it can't be set on an email by email basis, only an account by account basis. (Click the avatar at the upper right to switch accounts.)