How to connect Mining Rig Computer to Drill? As I did not try, I could not do it. I'm not saying that this is a bug, I just can't figure out how it should work.

I also noticed that the names of some parts of the Drill are not displayed correctly.

I noticed another unpleasant bug, if you place Drill Head in Drill, then break Drill, after that Drill Head simply disappears and does not drop out.

If there is an explosion next to Drill, only parts of it break, shouldn't it break completely?

Already fixed in dev, the update will be released later today. The guide book has been updated to explain how the Mining Rig Computer works and also has a setup screenshot. This video also explains it. Thanks for reporting.