Yes and No
As a licensed MSW (LCSW) you will be able to bill some insurances directly but you will always have to have supervision--that is not allowed to independently practice.
I dont know about specific charges, but there is a difference in what you can charge--in the midwest a definite difference in client demand--we have a lot of LCSW/LCPC but psychologists are always in demand
Ummm.. I'm going to have to disagree with Jennifer on the bolded part. In my state, the LCSW allows you to practice independently. I have the MSW LCSW combo, and will have had my private practice for 3 years in January. Although I certainly underwent supervision in order to get my license (many years ago), I have no supervisor now. I
collaborate with the psychiatrists with whom I share patients, but they do not oversee or direct my practice in any way. I carry my own malpractice insurance per the requirements of the managed care companies I'm on panel with (and because I have common sense). When I am stuck or experience a dilemma, I
seek out supervision because that is best practice (and again, because I have common sense). I am able to bill Medicare directly (and do), as well as Medicaid (but don't because my state's sucks and I refuse to work with it), and many private insurances.
Regarding charges, I set my rate at what I believed to be competitive in my area. This will vary depending on your location: rural areas are typically cheaper, urban typically more expensive. I'm in the Midwest; I have no doubt that my fee would be different if I was on one of the coasts. I work with some managed care and EAP panels, some people I know accept cash-only. Overall income will depend on rate charged, rate accepted (ie, sliding scale? managed care? full-fee only?), number of patients seen per week, individual vs group therapy, and probably some other variables I'm not thinking of- oh- like overhead expenses (rent, phone, office supplies, license fees, malpractice insurance, continuing ed).
Regarding getting into private practice, you would have to be licensed first, which is usually a minimum of 2 years of paid supervised clinical experience post-masters. I've only known one person who got their private practice going immediately post-licensure, and that was mostly because she has a niche (eating disorders). Otherwise, most people find that it takes them several years to get more experience, network, make contacts, etc.
There are a multitude of threads on this from previous posters, so I'd suggest you do a search. I know I have some really long posts about licensure processes, etc., which may be helpful to you.