my main question is if is posible to upgrade from avast mobil free to avast mobil premium without having my phone physically with me?
No, that is not possible since you can't tell the phone to install it without having access to your phone.
my lost phone has anti-theft rooted and I have maded connection to lost phone with Request Location already but I want to upgrade antitheft to use Record audio/take picture/get data command... can I just upgrade from my avast account?
As has been explained in the manual, you can only use certain commands if you have gave the permission for it. If you haven't while you still had the phone, there is nothing you can do about it now.
Since the location command is working, go to the police.
Report the phone as stolen and tell them that there is the option to locate it.
After that it is up to them to take action.