Those are all things you will develop a strength for as you progress. Kinda like hardening your confidence armor.
At first, i couldn't so much as wear tight jeans and a girl shirt without freaking out and having intense anxiety, I wasnt even wearing make up or a bra. Now I dress full time and I use the female bathroom all the time. Sometimes i get looks of curiosity or confusion, but people don't usually cause a big deal about it. I imagine that this is because Im only there to do what the inteded purpose of a bathroom is, and also because women usually are concentrated on a thousand other things to worry about whether or not you're a "dude or a chick".
People are gonna think what they are gonna think, what matters is what YOU think about you. Sometimes thats all it takes. I'm still just starting out and i have a lot of male features, yet i present female, i behave female and I firmly assert my certainty that I am female no matter what anyone thinks.
People wont generally be so straight forward or childish as to yell out "OMG ITS A GUY!" they will more than likely go no further than just gawking, anything else would be incredibly rude or childish and would more than likely cause them to make an ass out of themselves all on their own.
Its funny that i ran into this post because just last night i went out to a karaoke bar with friends and this old guy was literally RUDE enough to stand right in front of me and pull some random stranger next to him and say to him not even discreetly "Look to your right, look at that" and I was what was "on the right", the guy made a huge deal about me, and the other random patron was like "so? who cares?". Absolutely astonishing that this guy literally lacked the respect to consider that he was treating me like a zoo animal.
The more you do these things, the easier they will be to handle, and even better than that; you will be able to develop a sense of social behavior that exerts confidence. Back then I would stay quiet and avoid making eye contact or conversation with the cashier anywhere, but now if they ever chat me up, i chat right back and have a few laughs. Sometimes you just have to look at yourself in the mirror and say "I am me, no matter what anyone thinks."
You're just starting out so you have quite a ride ahead of you.
As for the whole looking older thing: that will change (at least it has for me), as the days pass i look younger and younger presenting as female, but currently it still makes me look older, probably also late 20's, and I'm 24 anyway so looking a few years older is no big deal. You will have a hard time seeing the female in your physical presentation because you've been staring at "male you" for the last 20-something years, so your mind has a burned in image of your male presentation. Some people will see you as female, others will see through you, others will simply treat you the way you are dressed even if they see through you. The point is to not place too much value on what others think of you and concentrate more on what you think of you.
Everything you're feeling is normal. I felt the exact same way the first time I ever began embracing and expressing myself

You'll grow out of it; the hormones help with those feelings ~ they did for me.