it automatically stops charging and runs of the power adapter once its full, and when theres a spike in power draw it will draw some from the battery intermittently. That's also why apple recommends you keep the battery in even when you are running off wall power
Yes, it's OK to leave it plugged in. You can't overcharge a Macbook battery. I kept mine plugged in and as a desktop for a year. I cycled the battery once a month. Now that I have a Mac Pro I use the Macbook as a laptop. My battery health is still 100%.