You are asking two unrelated things... And not providing any detail on which to base answers for either...
Could you join the site to be able to reply to this thread?
What phone? What OS and Firmware version? Preview for Developers or not? How long does the battery last? What did you change just before the battery life went bad? What App won't install? Install method: store, SD card, trying to sideload??? What error message on the failed install?
Help us to help you, please.