the one I know without having to look in the literature is 1)
Lemma 2.2.3 of http://arxiv.org/pdf/math/9908167v2.pdf
I think 2) is true as well (maybe you need to add the adjective tameness appropriately?) and for 3) there should be a result of Kresch saying that your stack can be stratified by quotient stacks. But I'd have to look this stuff up.
for 1) I should say etale topology.
for 2) I was thinking about this result (Theorem 4.4 and Proposition 5.1) by Kresch http://www.math.uzh.ch/fileadmin/user/kresch/publikation/geodm.pdf
for 3), the result I was misremembering was Proposition 3.5 of http://arxiv.org/pdf/1002.4372.pdf, and the first paragraph of the proof. (it's for stacks with affine stabilisers)
There is a paper by Edidin-Hassett-Kresch-Vistoli where the investigate when an Artin stack is a quotient stack. It turns out that this is closely related to the pushforward of the structure sheaf of a smooth atlas to admit a surjection from a vector bundle. Here is the review by Vezzosi. http://www.ams.org/mathscinet/search/publdoc.html?pg1=IID&s1=611835&vfpref=html&r=34&mx-pid=1844577