Question about Migrating Posts

So I am transferring all my posts from Site A to Site B through the Export/Import function. Site A became a hit through social media traffic but it has a bad domain name so I am moving it to Site B with a better domain name.

My questions are:
If I move everything to Site B,will all those posts in Site A that I moved be deleted?

I am planning to just redirect Site A to Site B since most of the links in social media are through Site A, is this the best option?