Erin, I'm sorry to hear you've found MO so negative in tone. There are a number of issues that have been brought up, both in the post and in comments, that might be useful to tease apart.

Let me start with re-tagging. I can see why you or anyone might resent others fiddling with their tags, and I do think it would be more collegial if others would (before eliminating a tag) ask first the reasons behind it. I'll qualify that slightly: if a noob comes in with a question about high-school level analytic geometry and applies the tag algebraic-geometry, then of course it means he doesn't know what that tag means to our community, and there doesn't seem to be a real need to discuss what he is thinking. But for someone with over 1000 points of reputation, and who holds a PhD in mathematics to boot, etc.: I'd say she should be asked first before removing a tag.

(Adding tags is probably less of an 'affront', although a polite comment such as "I took the liberty of adding such-and-such tag; hope you don't mind" would still be a nice collegial thing to do.)

That said, it's fine if someone who doesn't understand the point of a tag asks about it, and I don't agree tagging is (merely) subjective. Tags should be applied keeping in mind those users who filter by tag. Are those users likely to see the question as relevant and on-topic for that tag? If they don't, then they might feel their time has been wasted. (Let me put that more strongly: it is beyond dispute that many users are considerably annoyed by what they deem as improper tag choices -- why, there are two flags about precisely that in the moderator inbox, now as I speak.) So with that in mind, it should be part of one's routine to provide enough background so that hopefully all tags make sense to those concerned -- in particular, for a question ostensibly about transcendental number theory, some explanation for a tag like set-theory should be given.

This ties into the general issue of motivating and providing background for questions. I think a lot of users (not speaking particularly to you, Erin, but to people out there) might be a little uptight about this: MathOverflow seems like a hard-core or austere site, and people may feel they have to make their questions very concise and constrained (sometimes very formal as well), and they wind up not sharing why the question is actually important to them. So if for example

usually I am thinking of something more and I just want a reliable resource for my little question

then please consider instead sharing a bit of that "something more", if you can. If for example you intuit a connection between a question in transcendental number theory and issues related to set theory and forcing, then maybe say something about that if you can; people might find it interesting. (As an aside, Paul Cohen once said this: as a young student he was interested in number-theoretic identities like the Rogers-Ramanujan identity, and wanted to try a logical approach to them, by making an inductive analysis on the complexity of statements. "In a remarkable twist this crude idea was to resurface later in the method of "forcing" that I invented in my proof of the independence of the continuum hypothesis" -- More Mathematical People, page 50.)

In any event, I remember (now ex-)user quid pressing the importance of laying out background and motivation for MO questions, and I agree, and think it might help create more positive experiences at MO. The Help page also mentions this.

This enters into a more general question, which is sort of how I'd like the question of the OP recast, and which all of us should anyway ask ourselves:

How can I make sure my questions are positively received?

To begin with something simple: rendering formulas in TeX, as Andy Putman mentioned, is the norm and expectation in our Community. It's not a hard-and-fast rule by any means. But to state something obvious: if I take pains over the presentation of my question, giving it a professional appearance, then I transmit the idea that this question is important to me and I want others to take it seriously. Thus I agree it's a good idea to make use of the TeX software, routinely.

Relatedly, there is some expectation here that people, in addition to taking care over the presentation of the question, also exercise due diligence in researching the question a little beforehand (using Google, Wikipedia, etc.) -- and indications this has been done are usually well-received.

Speaking of this: if someone comments by giving a bare Wikipedia link, then in the first place let's grant the benefit of the doubt that he probably is trying to be helpful (and not snarky or sarcastic, unless he makes that plain). But in the second place it might mean he wonders why the answer wasn't found in Wikipedia, or why WP wasn't enough. Actually, not a few MO commentary discussions follow a pattern like this: a WP link is given, and the OP comes back and says, "Thanks. I did see that WP article, but I don't see how it quite answers my question, because...". And that would be a good response.

(On the other hand, I think it might help too, from the standpoint of netiquette, if commenters gave a little more than a bare Wikipedia link. There is every possibility that such comes across as a little curt or dismissive, or a slam dunk, or something like that -- even if you don't mean that. Imagine a friend asking the question; you might say something simple like "Might this be relevant? [link]" Or add a few words explaining the relevance.)

Erin also asks

I don't see what is the harm in keeping these questions up and just not saying anything unless you have something helpful to say

Well, the question of what we keep up runs into the perennial question of what the community considers 'on-topic' at MO, and as you know opinions vary widely. There will never be complete agreement about that. Looking at the number theory question in particular, I do think Mathematics StackExchange is the better choice. (And therefore the question should not be left up at MO -- one site per question, please.) Certainly it got a happier reception and result at Math.SE, and I'm glad you decided to post there. Something that worries me is that MO users may think Math.SE is a lesser site and are averse to posting there. I'd like them to reconsider. In theory there is usually a best SE site to post, and it's independent of where a user happens to feel most at home.

Looking at the beginning of your post, Erin: if it's really true that you feel put down by the responses every time you post a question, then I'm not sure what to say, except that (1) I'm concerned, and (2) I think you should consider making contact with the moderator team directly about this. Normally these things should be dealt with on a specific case-by-case basis, and not allowed to fester. Please also feel free to make use of the flag system if you think someone is being rude.

My greatest concern of all was touched upon in Stefan Kohl's answer: that your experience may have something to do with cultural attitudes and reactions towards women mathematicians. I take that possibility seriously. (Just now I was trying to track down Tonya Khovanova's blog article where she remarks on MO and experiences of female mathematicians; can anyone find it? I think we discussed it once at 'tea', but that site is now under lock. 'Mathbabe' may have also written about this.) As for myself, I can only imagine what it's like to be 'mansplained' at on a regular basis; let me close by saying I really hope this answer doesn't come across that way.