1- What does happen if the user logoff virtual machines? shutdown? Where can I find this parameter to configure?

normally is there is not issue within the desktop logoff tasks the log off will depend on your configuration of the pool (below are the settings), and pool type(floating or dedicated) ,and desktop type (dedicated or linked or instant clone)

as you know user either log off or disconnect , or shutdown

under the desktop pool settings: the option for these settings

-remote machine power policy : specify how VM behaves when the associated remote desktop is not in use

it can be

     1- Take no power action

     2-Ensure machines are always powered on

     3-Suspend

     4- Power off

then we have action the logoff or disconnect behavior

if user disconnected only , you can push user to log-off after time some time and you can stay connected(desktop will stay logged on and ) 

when user loged-off or the system logged him off some time , next behavior wheat will you do (delete VM, refresh or recompose )

2- what does happen if I power on the virtual machine directly from vCenter?

again this depend on the power settings of the pool explained above, if you select "take now power action" it will stay off , if you select "Ensure machines are always powered on" it will get startled again

I monitored the virtual machine and saw it powered down after 5 minutes , I tested it on another virtual machine and it powered down 10 minutes later and I did  it again and again and every time virtual machine powered down after a random time. I don't know this behavior is OK or no?

Can anybody clarify me?

(windows shutting down process need to checked any to see the processes and event viewer, also the profile and user data ,UEM, appvolume have effect on logoff and shutdown time as it have to grantee clean power off )

hope this answer thisquestion