No, you don't.

It should run on auto pilot. If you do a major change you might want to rebuild the site map.

Nope, unless you make major changes. Then you want to make sure the changes are picked up.

I don't think that you should have to check these things every week. Once you verify it the first time, you should be good to go. I tend to check webmaster tools often to see where I am in search phrases.. probably more than I should.