Maybe, but if they make it clear that they're not sponsored or endorsed by the project in question, it'd probably be considered nominative fair use, at least in the US: http://en.wikipedia.org/wiki/Nominative_use
They are soliciting donations using the project name. I don't think that falls into nominative use. It'd be really weird if I could use the logo of the Salvation Army to solicit donations for my own organization even if I intended to give some of the donated money to them.
I think so, yes. See Iceweasel[0], the custom Debian build of Firefox. I'm not sure that you'd be successful in using trademark law in this particular scenario though.