The tower thing is a possibility, but I don't see why it would be any more or less limited on location than something more elaborate. You can put up a tower literally *anywhere* that the ground will allow it, including some places that won't.
As for when you do it, it really doesn't matter. If you guys decide to rest for a while after getting the sword, you can build it then (or at least start). If you don't, you can have the thing be built as you pursue whatever mission is on your mind(s).
I can't answer the healing questions off of the top of my head - somebody else?