Can too. He can do things like encourage (and not veto) reversal of the horrible stem-cell research policy of Bushco. He can promote environmental causes. As far as a universal health coverage goes, it is not a short-term possibility, but we can aim in the right direction. The wheels turn slowly, but a fractional change in angle can lead to big directional differences down the road.
Can too. He can take a more progressive position on global warming, making it more reasonable for Americans to conserve. I'm not saying he will (since Big Business has lots of money) but he can. Of course, Jimmy Carter tried to get Americans to be altruistic and conserve just because it was the right thing to do. We see where that got him. I don't know if the situation has changed enough to make it any different for Obama.
Could. Probably won't. This is mostly in the hands of Congress, but if he came out strong for campaign finance reform, he could lead the country in that direction. Oddly, McCain has a better history in this respect, though he isn't exactly talking that up right now.
That will be a toughie. Of course, in the US, even our poverty is a giant step above the poverty of most countries. Reversing the trend (which has been ongoing since Reagan and continuing all through Clinton et. al.) of widening the gap between rich and poor is a doable thing. It would require some brave legislators and a popular groundswell of support. But like in the French Revolution, there will be a time when the poor people get tired of watching the rich eat cake, and no "commie" scare tactics or blaming illegal immigrants will work to blunt their outrage.