When someone says "thank you", you should either say "No problem" or "You're welcome". "No problem" tends to be only for informal things.
"Never mind" is only used when you begin to talk about something, but then decide that you don't want to talk about it after all.
When people say "Sorry," you can answer in several ways, depending on the context. If someone did something minor (like if they bumped me or spilled my water) and then said "Sorry," I would say "No worries" or "No problem" or "It's okay". If it was something serious that really hurt me (like if they gossiped about me or stole my favorite possession) I would say "I forgive you."
I hope that helped!