concerning the use of Mobile Connect, is it possibile to receive messages from customers to grab personal information to send in a second moment to an external system via API? What will be the flow? Can I set up a number which the customers will deliver the message to?
Yes, it is possible.
There are several ways to achieve this. You can do it with API for external systems, you can do it with AMPscript for Sales Cloud.
In your use case look into Next Keyword functionality and Info Capture template for SMS.
The way it works is you ask for some information from customer and customer response is stored to the attribute you define in the Info Capture. This is on the MobileConnect Demographics table.
Then you can use API to update the Contact in other system through this table with the value that was provided to the attribute field. The exact setup depends on how your integration is set.