I am presently using apc br800in it gives me almost 20-25 minutes backup and hibernates when in the last 5 minutes or so.

now coming to your 3rd point if your power goes at a scheduled time there is a work around.

use Shut Down Expert - Turn off & wake up your computer

now if lets say the power goes at 9 am everyday you schedule a hibernation mode at around 8:50 and when the power cut is there it will switch to battery but because there is no load it will run for almost 3-4 hours. now lets say the power comes back at 11 am then you schedule a wakeup at 11:10 am. so in this way you are able to start and stop the computer. Now what this software adds up more is the ability to start/exit programs in this way you can schedule wichever program to start at a specific time.