Powering on computer

maybe this can help :
http://www.tomshardware.com/2007/04/26/command_and_conquer/

extract from http://www.pcworld.com/article/id,124169-page,1/article.html

"To wake your system from standby or hibernation at a set time, click Start,Programs (All Programs in XP) Accessories,System Tools,Scheduled Tasks. Double-click the Add Scheduled Task icon to launch the Scheduled Task Wizard, and click Next. Select a program you'd like to run when your system wakes up, and schedule the task. On the wizard's last page, check Open advanced properties for this task when I click Finish before clicking Finish. In the resulting Properties dialog box, click the Settings tab, check Wake the computer to run this task, and click OK."

so its possible without additional tools if you use hibernate function.

Not really, if its shutdown its off, however as already mentioned there is only hibernate self power on etc.
If your out of the office over night not a good idea.
If your out of office for just a few hours why the need to power on? with some kind of auto?
you can use the power options turn off evreything except the hdd.

Check your bios many systems have an option in the bios to automatically power on at a certain time, some even let you choose what day(s) of the week also.

thanks