While the Support role doesn't require you to focus on farming and getting CS, there are other important things that you need to keep your focus on. It's often seen as one of the easier roles in the game and while I agree to some extent, it's not always as simple and clear-cut as some may think.

How much Cs should support have?

The numbers you should have in mind when you're killing creeps should be +/-8 CS per minute. Usually at the 10th minute you should be at around 80 - 100 CS on your lane. Midgame at 20 minutes you should be around 180 - 200 CS (220 after you master CSing and killing jungle camps while support freezes your lane).

Should a support hit minions?

Mostly you dont want to do it unless its a shove/crash into tower for reset or priority. Learn the lane minion manipulation stuff like freeze, shove, slowpush first. Also last hit when adc isnt there and you didnt back.