Can I use two phones as one phone with two screens? I have two phones. I would like to have all my files on one, but be able to have two open at once.

Can I set up the second phone such that it extends / adds a second screen to my phone?

I do not want to use BTSync or similar (the second phone has limited storage).
Clipboard sharing + cloud drive.
With those two you can do a lot with minimum setup.

For PC like experience you may share your peripherals. Not trivial, though. 

The biggest challenge is to sync the clipboard in a safe way. Most solutions are through WiFi router or internet and making a easy Bluetooth connection is a challenge.