Can I schedule startup and shutdown with different settings for weekdays and weekends?
You don't need 3rd party software. The OS X utility pmset allows you to schedule sleep/wake taking day of week into effect. I haven't tested it, but it appears you cannot schedule multiple repeating events on different times. You'll need to use cron to complete this task.

from man pmset

Schedules the system to automatically wake from sleep on 
July 4, 2009, at 8PM.

pmset schedule wake "07/04/09 20:00:00"

Schedules a repeating shutdown to occur each day, Tuesday through 
Saturday, at 11AM.

pmset repeat shutdown TWRFS 11:00:00