Hello! I'm a few days late to the party but I'm transitioning through NHS Wales so I can help, maybe! NB: I started medically transitioning as an adult, so I'm a bit sketchy on the details for under-18s.
1. On the NHS, you'll be able to choose Testogel/Testim (topical gel) as an alternative to injectable testosterone, and your endo may even recommend it for initial treatment (mine did, anyway). Personally, I buy Underworks from Amazon for about £33.
3. In Wales, it works a bit different to England (and possibly the rest of the UK) since we don't have any GICs over here. Personally, I just went to my GP and asked for a referral for gender transitioning services. My GP then had to go away and find out who I needed to be referred to, since over here it's not "the nearest GIC", but an intermediary - a psychiatrist, possibly a GID gatekeeper. The waiting list for that appointment should be as long as it usually is for a psych appt (this'll vary depending on where you live, but about a month? Maybe two??).
The psych appt... happens - they mostly just ask you about your transition goals. At this point it would be helpful to emphasise surgery needs, even if it's not a priority for you right now, because if they get any indication that they can drag their feet on this, they will absolutely take the mickey about it. After this, the psych will send a referral to the relevant endocrinologist, probably at your local hospital.
With any luck, you should get an appointment within a month or two (or however long it takes for outpatient appts at your hospital). The first appointment will just be for blood tests, general health checks, and to make sure your paperwork is in order, but as long as everything's fine you should be good to start soon after.
The psychiatrist will also send a letter to the local Gatekeeper (if applicable), who will apply for treatment funding and refer you to Charing Cross. I'm not sure if this is still true if you aren't seeking surgery, but I believe it is.
AFAIK, if you're under 18 when you ask for a referral from your GP, you'll be referred to Tavistock. That being said, I'm not sure (because Wales), and as long as you're comfortable doing so, it may be worth going to your GP to find out for certain. If nothing else, signalling your intent to transition now should help streamline the initial referral(s) later on.