i. I'm in the following situation: I'm adding a new user to a public group that already exists, and that user can't see data from that group. It used to work, but now it doesn't...

Hi @Karolina Ogłodek, Adding a user to a Public Group doesn’t automatically give record access. The group must be used in a Sharing Rule or manual sharing for the user to see data.

Since it worked before, please check:

•  If the sharing rule using this group still exists and is active 
•  Object permissions (Read access) on the user’s profile/permission set 
•  Org-Wide Defaults (if set to Private, sharing is required) 

Also try recalculating sharing rules. Hope it works.