To the OP, I'm going to guess you have a bad phone. The last 2 days I took my phone off the charger at 7:15am, then deliberately used it under heavy load (lots of game playing, browsing, etc) and by 9pm I still have about 25% battery life left.
As for Facebook, if I'm in the app and lock the screen, when I unlocked the screen it takes less than 1 second for the app to 'resume'. I never get a black screen.
And judging by how you don't notice much speed increase over the Lumia 710, I'm going to conclude you should get your phone swapped out for a working one.