<p>1) Almost always. As a general rule, you should consider an acceptance without funding as a rejection.</p>
<p>2) Pretty good. At some schools, applied math grad students get a higher stipend than pure math grad students. I'd imagine in the overall scheme of things, math is somewhere inbetween the humanities/less useful social sciences, and the fields with more money attached them (physics, econ, chemistry, etc), probably closer to the latter.</p>
<p>3) Almost always, yes. My friend temporarily had some weird offer from Purdue where he only got half of his tuition covered, but eventually they offered him a fellowship. But in general, they cover all of the tuition, and you only have to cover a few smaller things like health insurance, grad student union dues, etc (things the school can't directly pay for, for one reason or another).</p>
<p>4) NYU is the only school I know of that does this, but it's certainly possible. As I mentioned in 1, you should generally consider this a rejection.</p>