Credit card companies require making at least the minimum payment every month in order to be on time. Usually this is the larger of a fixed amount (e.g. $50) and a percentage of the amount owed on the card (e.g. 1% + interest). If you make at least the minimum payment each month, your card will report to the credit bureaus that you paid your bill on time, which will help your credit score.
Does this apply even if you’ve purchased less than the minimum payment? Is there a penalty for buying nothing with a card for several months?
If you purchase less than the minimum payment, you only owe that much.
And the only “penalty” for buying nothing is that they might close your account for inactivity. It’ll still stay on your credit report for 10 years (at least in the US). Usually they don’t close it if you use it at least once per year, but policies at individual banks may vary. I try to use all of my cards at least every few months so they don’t get closed.