HTC G1

i am a blackberry transplant does android support the type of email that comes to your phone as a message i think it is called push? email i just got a used g 1 to expose myself to android in a cheaper way before i dive in with a moto or nexus i am a T Mobile customer great service quality in Fort Worth Texas 3g
also is the awful battery life a fact with the g1 or all Android phones? i have installed app killer but still too soon to see a difference.
thanks