Here are the three questions I see that you're asking:
1) What to do about friends and people who know you who still use old name/pronouns;
2) When friends and people who knew you pre-T will switch more easily to male name/pronouns; and
3) When do you start to see changes from T?
To answer:
1) I correct them. Every single time I hear it. I'm not rude about it. It's natural, matter-of-fact, and even instinct at this point. I've noticed that some of my friends will correct themselves in the middle of a sentence or correct one another, and I don't even have to say anything at all.
If it's in a very large group or at work where I can't, I'll even email and say, "I'm sure it was inadvertence, but you misgendered me..." If people talk to me more about it (or apologize), I'm very understanding about the fact that it is habit and it is hard to adjust. I tell people that and I tell them that it gets easier over time - if you're aware of it, and that I find it helps peopel remember to break the habit if I speak up.
The only time it got more "serious" is when a super close friend thought I was expecting perfection and got more defensive about it, and I pointed out why it was so important (e.g., safety) and that it doesn't come naturally. It comes by trying harder. If I know I'm going somewhere that I think it would be "worse" if I were outed as trans with friends, I even remind them beforehand to be careful about names/pronouns.
Obviously, it depends on your crowd, but I think the normal "mistakes" people make are:
- letting it go for too long so no one thinks it's really a big deal
- setting artifical dates for when people should switch ("when I start T, then...") rather than based on when you are actually transitioning and/or wanting to be referred to as male in public
- putting people on the defensive or getting mad when people get it wrong
- expecting people to go part way and be able to switch back and forth based on where you're out
- hanging out with/staying friends with people who insist that they will never get it right and don't care
You CAN get things back on track again, even if you fall into any of these categories, but I do think it makes it harder.
2) I think Jay answered this best. People who know you pre-transition are not looking to gender you now (they already have), so they will see/refer to you as "You" and not as a guy. Even if they look dumb to everyone else. The closer they are to you, the longer they know you, the longer/harder it can be for them to see you as a guy, independent of how you look.
3) Most changes on T start to become clearer between 3 and 6 months. I wouldn't worry until 6 months. But your clock really only starts from when you have an appropriate dose/correct levels. That's why it is really important for people to get follow-up at 3 and 6 months after starting T.
I think the idea of androgen insensitivity is possible, but it's not always an all or nothing deal, like an enzyme deficiency. Some people have the ability to absorb more T and/or do more with it than others. You may just be one of those who will see slower effects.
I think you should make a list of all the changes you have had in the past 4 months to see if T is having an affect on you. Skin, hair, genital change, mood, voice, sleep patterns, disturbances to menstrual cycle, etc. Are you really not seeing any difference?