In some cases they have the same meaning: Person #1: Did you turn off the lights? Person #2: No Person#1: Ok that's ok it doesn't matter/nevermind Doesn't matter(more appropriate) Person#1 Should I take the bridge or use the other way? Person#2 It doesn't matter both routes go to the stadium. Nevermind (used more) Person#1 What did you want me to buy? Person#2 1 dozen eggs and a loaf of bread. Person #1 What? Person #2 1 dozen eggs and a loaf of bread. Person #1 You want me to buy legs???? Person #2 Nevermind(usually angry or upset) It's harrd to explain the contexts they are most appropriate in. These were the kinds that came to my mind right away.

They are interchangeable. It doesn't matter is more common, and maybe a little more polite.

They can each be used when you don't want to tell someone something, but "it doesn't matter" comes off a little more passive aggressively. It doesn't matter can also be used to mean its literal meaning in which case it can NOT be substituted for nevermind. Habría escrito esto en español, pero no habría sabido como!

'Never mind' is normally written as two words, no? Only time I've ever seen it written as one word is when referring to the album by Nirvana. And Cobain supposedly liked that title because it contained a spelling mistake. Maybe this variant is on the rise in North America, I don't know.

you mean there is no difference between them?