In regards to your two questions;
1. Do you reject all instances of he/she pronouns being used on yourself?
This depends what you mean by reject. If you mean do I always correct people who use the wrong pronouns, then no, not always. If you mean, do I always dislike when people use he or she for me: Yes, I always dislike when people use she. People using he isn't so bad but that's more because it doesn't happen to me every single day.
A good way to explain this would be if you imagine instead that when people use 'she' they are hitting my right arm, and when they use 'he' they are hitting my left arm. If people are constantly hitting my right arm almost every day (as is the case with being called 'she') my right arm is going to be pretty painful. If someone then hits my left arm (or calls me 'he') which happens less frequently, that isn't going to hurt as much because there isn't such a build up of pain.
2. Do you feel everyone should always ask anyone they meet their preferred pronouns before using any pronouns (even if they seem "normal")?
In an ideal world, yes. I realise that currently it would seem like a ridiculous concept to a lot of people, but it would make such a positive difference, and not just for trans people. I've been asked my pronouns once. An when it happened, I was genuinely shocked that anyone even thought to ask me.
One thing to consider is that someone's presentation does not always = their gender. Ie, someone may present feminine but actually be a man. There are many non binary people who present in a traditionally 'masculine way' but are not men, or in a traditionally 'feminine' way but are not women. Also, although generally there are only two perceived sexes, there are also intersex people who generally just get assigned one of the 'two' sexes.
On a related note, due to people not asking pronouns and just assuming all the time, I actually wear a badge on my work apron that says 'they/them'. I have had a grand total of two customers use my correct pronouns when referring to me, and one of them was non binary themself. I also have a similar pronoun badge on the bag I usually carry, in an attempt to get strangers in general to refer to me correctly. Unfortunately, I can only assume most people either don't see the badge or don't understand it, so I still get called 'madam' whenever I go to do my food shopping.
In regards to automatically assigning people an m or an f and struggling to see someone as anything other than that; you can approach that the same way you might approach correcting other automatic thoughts. Just as an example, as a child I would think negatively about other people's appearances. In order to stop that, I spent a long time just simply correcting myself every time I had those thoughts. If I had a negative thought about someone's appearance, I would tell myself that it was unfair for me to judge someone by their appearance. Nowadays, I rarely have those thoughts. But, when I do, I simply follow that same procedure to correct my thinking.
It can be the same with assigning an m or an f to someone. If you find yourself thinking that someone is probably an m, try to remind yourself that they could be an f, or even an x. It takes time, of course. I try my best not to gender people I don't know, in general. At work, if I need to talk to a coworker about a customer I won't use 'this lady' or 'this gentleman', I simply use 'the customer' instead. I do find that I often perceive a person's gender by their presentation (whether that means I think they're a man, a woman, or non binary). But I also remind myself often that no one can automatically know someone else's gender.
And as others here have said already, it's fine to struggle with they/them pronouns (or other pronouns) at first, but if it is constant then it is just as bad a misgendering a binary trans person.
Lastly, I think it may have already been mentioned, but just in case, there are many non binary people who do use she or he pronouns. This can be for simplicity, or due to the specific nature of a person's gender, among other reasons.
