Is there a way to control an android device with an external touchscreen?
If both devices are Samsung they have a brand specific app called SideSync which will allow you to link the two devices via a WiFi network. It's available via the play store or direct from Samsung. 
I currently have an S6 edge, a galaxy tab S and a Samsung Smart tv and can control the phone or tablet via the tv and the also the phone via the tv or tablet. 
Not too sure if you can control the tv or tablet via the phone as I've had no reason to try.
I have never come across an app which works in the same way if any of the devices aren't a Samsung but I've used this app with my current setup and with the old setup of S4, Tab 2 and older Samsung Smart tv I've owned over the last 12-18 months with no issues.
I hope this answers your question.