Can I have Gmail and Inbox by Gmail installed together I am a Gmail user but would like to try Inbox by Gmail. But.. I don't want to have Gmail removed as part of the "upgrade". 

Is this possible?
You can indeed! Inbox will give you a pop option to disable notificaitons from Gmail and get them from Inbox, or you can just get the usual Gmail notification. They are completely separate applications, both just happen to link to your emails, which are online so the Gmail app will have the usual layout, and Inbox has its bundles, previews etc. If you wanted you could get notifications from both of them (though that would be more of a pain I'd imagine)

I've been using it for a few weeks now with both installed and I have no conflicts bar one small one: Tesla Unread Plugin. This is an extension for Nova Launcher Prime that shows the number of unread mails/texts/missed calls etc over the icon for an app. On a rare occasion Gmail has a '1' over it after I've read the mail in Inbox. Opening and refreshing Gmail, or just leaving it alone for a few minutes solves it.