Mail not opening to Inbox

When you are viewing an email, rather than going through what you describe, in the upper left corner of the screen you should see a prompt to return to the inbox. When arriving on that Inbox screen, you should see a prompt to return to the account the Inbox is for. That brings to a screen of all your mailboxes. From there, just swipe up on the screen to close mail. The next time you tap on the Mail icon, it will open to the Mailboxes screen and you can choose the account you wish to view. What you are doing by swiping up partway and then swiping off again is force closing the mail app. That is not necessary.

If you get to the Inbox screen, then I'm not sure why it would open the last email read. When you are opening mail, are you opening from the notification, or are you just tapping on the Mail app icon? It does not make sense that it opens the last read email.

As far as the force close, the app is not really running in the background, it is suspended when you close it. The iPhone does a great job at managing RAM, so it is not creating a problem for you with having these apps suspended in the background. If your iPhone needs more RAM to operate, it will take what it needs. Apps should not be force closed unless they are not working correctly. It actually takes more time and power to open them again from this force closed state than it just to just swiping through your suspended apps and tapping them there to open them. Much easier to manage and that is how it is intended to work. However, I'm not judging how you do things, just providing information. It is up to you of course how you continue. I've not seen the behavior that you describe in the way that I read my mail.