I'm trying to wrap my head around how internal links (between posts) are handled when migrating from another forum software to discourse. The sparse information I found on meta seems to be in part contradictory, which is either due to me not understanding stuff or some information being outdated (e.g. because a permalink UI was added to site settings or import scripts were improved).

So here's what I'd like to clarify:

1. Do (most) import scripts convert (i.e. rewrite, not redirect) internal links?
2. Is it correct that the the purpose of permalinks is primarily to redirect incoming traffic? 
3. If so, do permalinks have any relevance for making sure internal links work? 
4. If, for whatever reason, internal links were not converted upon import (i.e. the links on the new forum are pointing to posts on the old forum), is there a way to retrospectively rewrite those internal links so as to get rid of all links pointing to the old site? 

I understand that additional problems exist when old an new forums are on the same subdomain, so to keep thinks simple(r), let's assume that the new forum is on a different subdomain.