HRT depends on your local laws and who you see. I was put on HRT so fast I was initially shocked and kinda' wanted to slow things down... I mean, we hadn't even kissed yet. American law no longer requires therapy to start HRT, but many doctors still do. They tend to be the doctors with less experience with HRT or moral qualms about it, in any case some doctors still want a second opinion from a mental professional, and if that is all that is available near you, that is a hoop you must jump through.
You said, "Mum" instead of, "Mom" which makes me suspect you are not in America. Your laws are likely different, and without further information (which you are NEVER required to provide) it is hard to give you more info than what I know about my own laws and experience.
Ok, the family question. Again, and you probably know this, every family is different. Different trans folk have different expectations from their family. I can again, only really relate my own experience. Most people have a good hunch as to how their family will react before they come out. That said, there will be surprises.
I came out to my fiancé (now wife) before we were married. It only seemed fair. She also knew about HRT from the start. I came out to my parents the next year, and waited a month after HRT started to tell them I was transitioning. I wanted to make sure the decision was mine alone, and did not need their input or concern clouding my judgement. I also wanted to wait until I had been on HRT long enough to know that I intended to keep going. I didn't want to tell them one thing and then change my mind.
I knew in my heart, they would love and accept me no matter what. They stayed with me through drug and alcohol abuse and a suicide attempt. Transition is mild in comparison, and as odd as transition may seem to them, the instant gratification of having a happy child (finally) makes up for it.
No siblings or children to worry about. No hurry to tell my extended family. I don't need to present as female to quell my dysphoria, so depending on how extreme HRT physically changes me, I may not need to tell anyone I do not want to tell. Once you come out, you can't go back in and, for some people in my life, knowing I am transitioning would bother them but knowing I am transitioning but continuing to present as male would break their brains. If they ever need to know, I will let them know.
My mom doesn't yet understand why, if HRT has fixed my brain already, I would want facial hair removal, or a reduction in upper body strength. My wife also seems confused at times at how willing I am to let little bits of my masculinity fall away. My dad hasn't mentioned it since he found out, which is his way of saying, "It makes no difference, you are still my child, I love you, and I am more interested in how your day was than how tender your nipples are."
I am willing to bet that many of us who have successfully come out to loved ones, are surprised at how quickly the conversation moves away from us and our transition. Once accepted, it really isn't a focal point or major conversation piece.
Some general advice:
Every family is different and timing is important. Especially if you think there may be a negative outcome. Good to pick a time when you can better handle rejection and have some time to recover. It is also good to pick a time when they will have time to process the news. This is big stuff. Be prepared for far more or fewer questions than you anticipate. Consider being efficient with your words, you can overwhelm even your biggest advocates with TMI.
For most, coming out and telling people about HRT is frightening almost every single time it involves someone close or important, but I am finding it to be quite the mature thing to do. It is empowering to tell someone you are finally starting to discover your true self! That you are happy. That you are doing this for yourself and nobody else! It is empowering. Really. The power that can be generated by such honesty has actually felt kinda' masculine to me, in a good way. It is a power I never wielded as my former shell of a self.
Good luck. Let us know how it goes.