This chap turned up, walked around for a while and then just decided to stay here for 23 in game years, in the same spot. I cant click on him at all. Has anyone experienced anything similar?

Heya, sorry you've ran into this issue. 

This is a known issue where if the museum is destroyed with a Mimic Plant in it, this mimic sticks around. We're working on a fix for this bug which we'll release as soon as possible.