To shutdown:
As above, there is already a shutdown.exe program in Windows.
Next bit is to set it as a scheduled task:
Goto 'Control Panel'
Double click on 'Scheduled Tasks'
Click 'Next'
Click 'Browse'
Goto to your root-drive (commonly c

and wind the 'Windows' folder.
Find the 'System32' folder
Find 'shutdown.exe' and double click on it.
Tick the boxes you want to apply (I would assume daily)
Change all the options you want to change for the time etc.
If you log into the PC, then you will need to provide the username and password.
Tick the box to change advanced settings, and click on 'Finish'
A box should appear, and the first tab name should be 'Task'
At the top, there should be a textbox with the word 'Run:' next to it. Next to that should be the path of shutdown.exe.
Add to the path " -s" (including the space). So mine looks like this: "C:\WINDOWS\system32\shutdown.exe -s"
Click 'Ok' when your done.
That should be it
If you want to test it, when in 'Scheduled Tasks', right click on the shutdown task and click on 'Run'. This will force run the task, so it should work straight away regardless of the time and date.
Note - To cancel the shutdown timer, click on 'Start' > 'Run'
Type in cmd in the box.
Then type shutdown -a
That will abort the shutdown task.
AFAIK the only way I have seen to start up a PC on its own is to use Wake On Lan. This is when you run a little program that forces a PC (on a network) to startup.