As far as I know (not on T yet myself), this page is a pretty good overview of the effects of T and various questions one might have about it :
http://www.ftmguide.org/ttherapybasics.htmlI assume that in most places you'll be required to provide a letter from a psych to "prove" that you're trans in order to get access to HRT, so you may skip your usual doctor and go straight to a psych and then go get your prescription from an endo once you got your letter.
As for your mom, unless you're somehow legally bound to her when it comes to medical matters and require her knowledge and/or approval in order to see a doctor or get treatment, if she doesn't approve then just don't tell her. Just say you're going out somewhere with friends or whatever and go to the psych/doctor. If you're a minor and her involvement in your medical decisions in legally unavoidable where you live, I'm afraid you'll have no other choices than waiting until you reach majority or trying to change her mind.
On the voice part : I don't know the proper terms to explain it, but one thing that helps is trying to make your voice comes out from a lower place physically - like making it resonate in your thoracic cavity instead of your throat. I don't really know how to explain it, but if you pay attention and practice a little you can "feel" where it's coming from. It feels a bit like using the same muscles you use when expectorating (coughing from your lungs), as opposed to using the muscles in your throat and the back of your mouth, which are the ones used when speaking in a lighter voice. Well that's how I feel it anyway, it may not be physiologically accurate at all