Sorry for being so noob in this field... but I just want to know ... Can we use TOR using some web interface, e.g. hidemyass.com ?
Yes, this is possible but I assume you want to use tor for anonymity.
In general this is the idea of TOR:
You always want to use encryption, because the actual data going over the line may link to you. And so you do not want to connect in plain text to a web interface, where the web interface connects to TOR. The web interface may contain a backdoor, making you not anonymous.
Instead use tails
https://tails.boum.org/ or the tor browser bundle
https://www.torproject.org/.
Another option to be anonymous would be to use VPN services. You could get several VPNs and connect one to the other. This is not free however, it is generally much faster;
When surfing with TOR is it completly anonimous?
It depends. The final node know what unencrypted communication (plain text data).
For example if your final node is skype:
You must realize that al though the communication going over the tor network, with skype all data is being recorded, stored and analyzed by microsoft & friends. (Skype contains lots of spyware, you can see it when looking in the data files which you can find in \%AppData%\Skype\ you can open these files simply with notepad. In addition there are the PRISM files leaked; ). If you have a conversation "Lets meet in LA next Tuesday 2pm" they know that, despite you running it over the tor network. So the final node is very important. Just using tor does not mean you are anonymous, but you are harder to find than using nothing.
I heard some the TOR servers are run by secret agencies of multiple countries... true ?
TOR servers can be run by anyone. There are groups who want information by any means possible, this includes secret agencies but also others.
Whether this 'means' is technical, psychological, physical or other means.
