You ask a subjective question and here is my (very) subjective answer. I have TA'd a couple of math lecture courses for non-math people and this is what worked for me.
Let me describe an exaggerated worst case scenario:
There are two sides: On one side there is evil math. An utterly useless subject which is for some reason very hard - obviously just to been mean.
On the other side are the innocent students. Actually they are very smart but just not good at math. Why is this annoying subject destroying their average?
The lecturer is usually on the dark side. He/she really believes that people should learn math since it's useful. In his/her clouded point of view just learning for the exam is pathetic. He/she deliberately includes very hard problems in the exam, just to make sure many will fail and just the very best will pass.
The key for me was to somehow manage to be perceived as an ally of the students. You are the person who is actually good at math but understands the students. Then the students will feel more comfortable asking their "stupid" (in reality simple but helpful) questions and actually expect that they might learn something from the answer.
In my very first lesson I just ask the provocative question "Who thinks math is useful?" and then "And who thinks math is actually fun?" If enough people answer those questions with yes you can just forget everything I just said and have a good time. If most people say no, I continue with something like:
"Here's the deal, I am one of those people who thinks math is both, useful and fun, but I understand that some of you might think differently. Actually this is not really a problem since we have the same goal, namely that you score as high as possible in the exams. This is what counts, right? If we have the time I will maybe sometimes try to say why this is all useful but first of all I will try to give you enough tools to ace your problem sets...
Something like that.
Then I think there is a big difference how math people tackle a problem than how many non-math students do it. We try to understand the problem first, find a solution conceptually and in the end writing down an "algorithm" to solve these kind of problems is pretty clear.
When I am asked a question in a lesson how to solve a problem, I start with explaning the recipe without saying to much about the reason. In theory the students should be able to plug the problem into the mechanism and get a solution without thinking. Obviously I explain afterwards - following the steps of the solution - why this all works. I sell this part as "a way to memorize it". I am usually amazed how many people actually listen to the second part (one could expect they just stop after part 1), but apparently once they know that they have the tools no matter what they are able to follow a proper explanation with less pressure.
Obviously this is all very subjective and perhaps pretty declamatory but maybe it helps.
Edit To actually answer your three questions:
They treat you like garbage since they think you are one of math's evil minions who is there to torture them. Once they realise that you are actually another human being who is just doing his/her best to help they will treat you more gently.
You are super good at math, right? For you all of math is very easy and you obviously never make mistakes. Wait, no? The math you are learning makes you struggle as much as they do? Sometimes you are incredibly frustrated after starring at a paper for days without making any progress, aren't you? Let them feel that! The math they are doing is very hard (for them), you are obviously at a different place but that doesn't mean you can not totally relate to them!
Obviously it is hard at times but if they ask the very simple questions then you can help.
Yeah ok, you disagree so far, but who cares? Your common goal is a good result in the exam. You might be somewhat happy if they appreciate what you are doing but if not, you are satisfied if they just realise that you might personally like it for some reason. Potentially you will never agree, but in the end it's also a matter of taste.