1 Yes, but there is no advantage in that.
2 No, got to pay the license fee anyway.
3 Easy. Mendix has good tooling for rest, soap and odata. As well as modules to connect to databases (if you really need that)
Also..
although running on-premise may look attractive at the you would be advised to evaluate the impact on the deployment process. It is substantially more complex and time consuming than deployment to the Mx cloud. The financial business case may not stack up once you factor in the additional man hours required for each deploy.
As I understand it, organisations choose on-premise mostly for security reasons / internal architecture requirements rather than as a cost saving measure.