1. You are correct, the permalink is created when you leave the title field. However, I believe you are able to edit the permalink until you publish the team. Yes, you are well-served to have your permalinks squared away before publishing.
2. Thanks, for the screenshot. The code that generated that warning (not an error, BTW) is dead code that has been removed from the trunk, awaiting the next release. You can either comment that line, or load the file from the plugin’s trunk on wordpress.org, or I can send you the file.
3. Yup, not all the MSTW CPTs behave this way. As I hinted at before, the team CPT in Team Rosters is a bit janky in this regard. It’s on the list for the next release. The two guys who were most affected by this both load their teams from CSV files, so they simply deleted them and re-imported them. Sorry I don’t have the time to make this better at the moment.