I'm up to lvl 6 on diamond refining research in the base development whilst my institute is lvl 10..

Diamond refining will give you a small boost to the speed at which you gather diamonds. Diamond gathering is very slow, the speed should be above 0 though. This sounds like a glitch, are you gathering them anyway even though the rate says 0? If so it may just be that the number is not displaying correctly. Try restarting the app to see if it fixes?

If you are not able to gather at all then report this to the game support so that the devs can look at the problem.