I don't care - No me importa
I don't mind - Me da igual
For example:
1. - No me importa lo que habla gente. Lo único que me importa es que tú me amas - I do not care what do people talk. The only think that I really care is that you love me.
2. I am going to invite my friends tomorrow for hanging out. - Voy a invitar a mis amigos para que mañana pasemos un tiempo agradable.
Ok, do whatever you want, I don't mind. - Ok, haz lo que quieras, me da igual.
I hope this helps. If you have any questions more, feel free to ask me.
Have a nice day.