I'll take a swing at #1, to build on what Genia has already said:
In pitching FIRST to companies that fall beyond the proverbial "sponsor safe zone" (as in, a sponsor that can see the direct benefit of FIRST on their business), I have found that FIRST often loses out to organizations that fulfill basic needs to the underprivelidged. The reasoning? "If students can afford to compete in such a costly-looking competition, they are nowhere near underpriveledged, and my money can be better used to....."
So, why would someone not want to give to a robotics competition? A psychologist named Abraham Maslow may have something to say about it. His claim to fame, "Maslow's hierarchy of needs", contends that as humans meet 'basic needs', they seek to satisfy successively 'higher needs' that occupy a set hierarchy. (
Wikipedia's listing is a good starting point in finding out more). According to the heirarchy, FIRST could be classified under "safety needs" (referring in its most basic terms to the "security of employment"), but they still fall above "physiological needs" (the need to eat/sleep/etc).
The bottom line? People with money to give naturally would rather give to focus on basic needs. Although FIRST has an advantage by its unique way to excite students, its showiness can also serve as a deterrent because the beneficiaries of the program do not look underpriveledged to Joe Public.
Thus, statistics to prove that misunderstanding otherwise are extremely important to show the amount of good work that FIRST does in multiple socio-economic levels.
I hope this helps a little!