First of all, AP Stats is absolutely helpful for a pre-med major. Most bio, chem, etc. programs require a statistics class, sometimes two, and AP would fill the requirement for the intro level class.
If you aren't sure, look at the requirements of a few colleges around you that you might be considering. But I bet they include a Statistics course.
However, Calc II is also very useful and usually required as well. Yes, taking it at a local community college would be functionally the same as taking it at your high school as far as credits go. The credits will transfer and you will not need to take the class again. Community college classes are much cheaper than university classes, although typically much more expensive than an AP exam.
The class' structure depends on the college, but most college math classes are held 2-3 times a week (usually Monday, Wednesday, Friday or some other set of days of the week). The average college class requires you to be in class for 3-4 hours a week total, so many classes are 1.5 hours for two meetings a week and then 1 hour on a Friday. Alternatively, they may have two 2 hour sessions each week or even one 3 hour session one day a week. If you look up the course catalog of the community college, and search for the equivalent class that is being offered this fall, then it should have that information in the course listing.
College classes typically expect you to spend 2 hours outside of class for every 1 hour in class doing homework and studying for tests. So if the class is 4 hours a week, you should plan out 8 more hours for homework for it. Community colleges are sometimes a little less than that, but that's the average.
Do keep in mind that college courses only run for a semester, not a full year. So you should have something else planned for the other semester. On the other hand, you could plan to not take a math at all in the fall to have more time for your college applications, and then take the Calc II class in the spring when your applications are done.