I would first say that, if I were in your place, I could never have well said my feelings as you have conveyed.
Note: English isn't my first language either so generally when I'm writing, I often make uses of "/" because of confusing words.
What you talk of is the very fine balance and that is what is both the beauty and the beast for this community. The closest analogy I can tell you so you can relate is that think of it as "Friction"-The necessary evil.
As both are difficult and appeal to a very narrow and specific audience.
As far as MSE is concerned, I'd differ. You see, at $\geq500$ rep, one gets access to "First Answer", "First Questions" and "Late Answers" queue. So, I've seen that very basic questions to quite complex problems, all are entertained here. So, I don't know how you can make such a claim. On various meta-posts, in consensus, I've seen that most high-rep users are of view that basic can't be well defined. Leaving the very few who think this site is too good for basic questions, generally speaking you shouldn't face any problems.
the community members are extremely mean and and unhelpful to each other and are gate keeping these fields with an iron fist especially to beginners.
Immediate downvotes for simple formatting errors, wrong usage of latex, closing posts because of 'similar answers' that in reality are far from the same.
If "mean" means downvotes or closing of questions then that isn't mean but manicure/hygiene. See, though I'm not comfortable with downvotes as I think it spoils the mood but those who do don't do it because it will spoil somebody's mood but so that the user may know that their post isn't up to the standards.
"Iron fist new users" sadly this might be true. Since I have access to first questions queue so sometimes while reviewing I take interest in some questions. I've seen most of such questions getting closed.
Read the chat under this question and perhaps you'll feel better.
In this post the questioner hadn't made any attempts to improve their post yet. Maybe the question doesn't really mean anything to OP?
In this post I feel iron fisting to a great extent. The question got closed pretty fast, and no one was commenting! After the question was posted, 8 mins in I posted my comment to improve the post. 2 mins later it got closed! Too fast! But still alright. I liked the question, so I added a very basic working and resolved the closing reasons. The OP too accepted my edit. But to my dismay the edit was later rollbacked as it wasn't OP's original working! I don't get it. The OP accepted it. Wasn't like forced upon them as it would had I had more than 2000 rep. When my edit was rollbacked I added another comment but I knew it shouldn't make much difference now as the new user saw a working on their post and them also saw it disappear, anyone will get confused by this. Perhaps here OP was indeed demotivated. The user is NEW so give them some space, that when another user is helping them kindly let them but the community thinks otherwise. Instead I was told to not repeat such a thing. Anyways, if the question stays closed for long or deleted, then I plan to ask that question myself (or not if I solve it myself.)
Basically, in some cases even though some users want to help the new users, the community don't see it in good light. Fine to me. I now just bookmark such questions or take a screenshot to save for later. But hope a positive change in this direction.
People who answer questions are unreasonably harsh to the exact audience that should be given compassion patience and empathy.
This sometimes may be the case. I think the issue is that the new users don't know what to do in such a case as something similar happened to me. When a user is harsh to you or bullies you, then you must (not should) raise a flag: 
besides any comment or 
under any question or answer. The moderators who are the power rangers of this site will see to it and take necessary actions. In my case, I saw the user suspended from the site for some time. Though sometimes the loss they cause you might not be undone.
Latex is not at all intuitive or easy to learn.
That's true for anything of one doesn't wants to put their least efforts into it. As far as basics are concerned, it really doesn't take too much time. If there is something too complex that you think you just can't then if you post it as a pic, many users are ready to entertain it as is and some will even to convert it to $LaTeX$ format.
Students are stressed and often desperate to reach out to this site for help and it often means that there is no accessible alternative.
I agree that MSE is the best.
Local formatting and language barriers often make it tricky to communicate successfully .
In this post I asked the user if am by mistake/unintentionally looking rude and they told me better alternatives to frame the sentence.
Similarly in another post, I saw interaction between 2 users and the OP there already told that she is using a google translator as a caveat in case the other users find some strange errors.
Hope you don't have strange expectations of this community of allowing questions be put in all sorts of languages or that any level of broken english will entertained.
If that's not the case, then this IMHO not much big of an issue.
If post get immediately downvoted for easily fixable causes they will never be seen or answered.
If causes ARE easily fixable and if they aren't fixed by the OP, then the greater blame lies on OP perhaps though if I see that post, I'll correct the easily fixable causes.
Also, downvotes doesn't mean they won't be answered and neither closed mean they can't be re-opened.
And to that i only have to say that i feel sorry for the people who need to feel special through math and as a result try to keep it that way by pushing both beginners and advanced learners out.
If you read this thrice, then, you'll feel that maybe saying so is rude/mean. People who are prodigies, A or O-grade students, PhD holders and believe it or not, even Nobel laureates have all positively contributed to this site to make it even better.
If a question is TOO advanced then I guess Math Overflow is a better place to ask them.
Any beginner needs to know the following before asking their doubts:
Welcome to Mathematics Stack Exchange! As this site is meant to be a useful repository rather than a Do My Homework forum, it's common courtesy to show what you've already tried, and really narrow down what you're struggling with. Most people here are glad to help once you've adequately motivated the problem. [Quick Guide](http://math.meta.stackexchange.com/a/34067/21813) to attracting answers and preventing your question from being deleted. Good luck!
Above is already mentioned in comments but I'm still repeating.
This said, you'll find all sorts of users in all sorts of mood. Some always happy, some always grumpy, some always very helpful, some very picky, some downvoting easily, some who are too conservative to downvote, some who upvote easily, some who don't and some who had a really bad day and then they open MSE! or some ... (so on).
In closing id like to thank the ones that set the good example that give good and helpful feedback and that are polite considerate and patient. You are the ones that make this community feel more welcome and approachable.
Well... Myself and on behalf on other MSE members (though no one asked me to :P): Thank you and you're Welcome.
$$and` and\frac{}{}`. $\quad$ "language barriers often make it tricky to communicate successfully" Bothering to punctuate with periods and commas, and organising Questions into paragraphs (as opposed to vomiting repetitious incoherent streams of consciousness whose lack of basic punctuation compounds the difficulty of deciphering the text) really goes a long way, $\endgroup$Welcome to Mathematics Stack Exchange! As this site is meant to be a useful repository rather than a Do My Homework forum, it's common courtesy to show what you've already tried, and really narrow down what you're struggling with. Most people here are glad to help once you've adequately motivated the problem. [Quick Guide](http://math.meta.stackexchange.com/a/34067/21813) to attracting answers and preventing your question from being deleted. Good luck!$\endgroup$$$and\sine(backslash) and\frac{}{}. $\endgroup$