If I rent and download a movie from iTunes onto my MacBook can I then watch it offline or do I have to have internet connection to watch it?

You should be able to watch it whilst offline - though some people (though I think that I've only see it for iOS devices) have said that they've need to be online when first starting to watch a rental, so you may want to watch a few seconds whilst you still have internet access ; after starting to watch a rental you have 24 hours if you are in the US, 48 elsewhere, before it expires