Communication options with SharePoint and the world

I have just started with SharePoint. Made a CRM system for our own company with help of the SharePoint suite found in Office365. This is mostly a 'getting to know sharepoint' exercise.

Now I'm starting to wonder: what are my options regarding talking to the world? We have a time tracking system, which supports API call's. We use MS Dynamic NAV for accounting, which also supports API call's.

Does sharepoint support API calls? Can I connect to the sharepoint SQL and work that way?

I'm actually thinking about connecting our custom made CRM system with our time tracking system. Can I easily populate/update items with data from REST api call's? Or should I program my own 'connector' which talks directly with sharepoint's SQL database?

Regards, SharePoint newbie