In my experience the Macbook Air is the best bang for your buck in terms of weight, battery life and speed. The Samsung Series 9 is really the only one that comes close in those 3 areas, and it's more expensive. Full disclosure: I own the new i5 13" MBA and think it's the best purchase I've made in a long time.
Yup, without question. The only thing I'd warn you is that when you're doing heavy work (video encoding or lots of heavy compilation/running) or heavy play (lots of flash), the battery life will probably be just under 5. Not at all like the 7 they claim, which is really only for casual surfing where the processor is bored out of its mind.
Good question, I don't run a lot of those apps but I do Ruby/JavaScript development on it and it feels faster than my i7 MBP (probably because the MBP has a 5400rpm hard drive). My guess is that you'd be fine, the only thing I can think of is that the Intel video card might slow you down in graphics intensive work in Photoshop.
Seeing as how I've done most if not all of those things on a secession of laptops from a Powerbook G3, G4, plastic Macbook and a MBA, it's more than enough.