So i won't be able to apply for adsense if i do buy domain mapping?.
Correct - no Adsense nor can you sell your own ads - they do have a program called Ad Words that you can apply for - but you need a ton of traffic to make even Pizza money
Note on Ads: most bloggers don't even cover the cost of hosting with Ad revenue
Say i purchased a domain on godaddy, could i export my blog and still edit and move new posts to that site from wordpress?
You can move contents easily - Export from your blog here - Import to your blog at another host - you would need to set up the Widgets and things in the sidebar and any header stuff etc as that will not export - but no extra software needed
Also, is domain mapping automatic?,
Domain Mapping is not Automatic but it is not very hard - you have some boxes to fill in and values to change - usually takes a few minutes and then some time for the changes to reach the far corners of the internet (24 to 72 hours for everything to calm down)