The project behavior you describe is likely due to the "resource share" you assigned to each project through BAM or the project webpages. You enter this as a numerical value, then BOINC Manager interprets it as a percentage that it will attempt to adhere to--though it will not be a cut-and-dry even time distribution. It's a floating average that is affected by a number of factors, including the work supply from your project(s) and any changes you make to the projects you have attached or their resource share. I wouldn't worry about that part too much, BOINC does its best to try and even everything out, but if you want to give more work to a particular project then you just increase its resource share until you have something resembling the proportions you want to contribute.
Another preference that will affect this behavior, is "Switch between applications every" xx minutes. If it's really bugging you, you can try changing this setting, but in my experience you probably won't even need this unless you have a high cache setting with extra work pre-loaded. I usually run my "Connect to network about every" and "Maintain enough work for an additional" settings very low, so BOINC doesn't download more work that it can currently process, in which case you shouldn't really see it switching at all.
Regarding your team, BOINCstats combined will show the team that you a member of at the most projects.
You could always post your settings here in the forum, but there really aren't any "correct" settings. You have to find a balance that makes BOINC do what you want it to.
Synchronizing with BAM is only necessary when you want to manually update a host if you've added or removed projects via the web interface, and even then it's not totally necessary as your host will automatically contact BAM on a set interval.