1) since miner is based on cgminer I should be able to monitor it with the regular cgminer api commands? Is this correct? e.g. stats command
Yes.
2) the controller controls several miners? therefore, i cannot send ssh commands? so my only option to restart miner is through the api?
Yes, one Controller can control up to 20 miners i.e., up to five miners on each AUC3, with up to four AUC3s per Controller.
The Controller uses OpenWrt as its operating system, which itself uses Dropbear as its built-in SSH server. Simply configure Dropbear according to your needs (it's enabled by default) through the Controller's web interface and you'll be able to connect to the Controller via SSH.
Canaan is something new to me so I didn't know exactly how the controllers worked.