If you have a blogspot blog and you want to have a different domain name lead to it. how do you get it to not say domainname.blogspot.com but the actual domain name only?
Buy the URL from a place like Go Daddy, then follow the instructions they give for using their interface. Takes only a few minutes to setup, possibly a few hours to propagate. You wont need to purchase hosting.
Redirect and mask the URL. Again, whatever platform you use will have their own set of instructions. I recommend Go Daddy since they support SOPA and us God fearing folk support the SOPA.
I don't know what exactly you mean with this. You should not "hard code" the URL into any page. Basically, the URLs should reflect where the browser's location is. As I understand it, BlogSpot only displays URLs when you've somehow added that in the blog code. You should not be seeing the old URL when people click or put their mouse pointer over a link. Show us an example.