[RAM Concept API] Is it possible to use API script to open and run .cpt files

Yes, the API can be used to run files. Refer to the API documentation in the program help menu. 

Do you know if we'll get full API for Concept in this next update?

All users have full access to the API, but the API does not cover every single function of the program. 

Do you have any ideas when can we expect for that?

I don't understand what you are asking. The API is already in the current release (and the prior release). If there is some specific feature you want added to the API, please let us know exactly what you are trying to achieve, or post to our Ideas channel. 

I don't understand what you are asking. The API is already in the current release (and the prior release). If there is some specific feature you want added to the API, please let us know exactly what you are trying to achieve, or post to our Ideas channel.