1) That message appears because you have to set up the options of the plugin Rotating Tweets (Twitter widget & shortcode). Go to the page Settings > Rotating Tweets, follow the steps and set up the Twitter API Settings fields.
2) Maybe it could be some little problems in the import, but that does not mean that everything has not been imported.
3) I don’t know what it could be the problem.
4) I have made a lot of tests with this theme and I haven’t gotten this error ever. The checking when this error happens, it is when the copyright text is loaded. You can set up this text from the page Theme Options, in the tab Footer & copyright.
Anyway, if you want, you can create a new user for me in your admin panel. In that way, I can check the errors better, and try to resolve them. I have done this with other users and there were not problems, so you can trust me.