Benvenuta, Anna Lisa.
All three words are nouns and verbs. I assume you are having a problem differentiating between the verbs, since the nouns are not likely to be confused.
'To mind' and 'to care' both mean to be concerned or interested in something, and there is considerable overlap, but they are rarely interchangeable. There are a lot of nuances to get used to.
I care about my family. I don't care for blancmange.
Would you care for a cup of tea? I don't mind if I do.
I care about appearances. I don't mind looking ridiculous/I don't care if I look ridiculous.
'To matter' is not used in the same way. 'Something matters' means something is important/significant. If it's important to you, you probably care about it.
If you say 'I mind' or 'I care' you are expressing your thoughts about something. If you say 'I matter' you're talking about yourself.
Student or Learner