Is floydhub the right place to deploy such a server?
The max uptime available for an endpoint is set to 7 days, after that, you will have to relaunch/restart the machine. However, we can modify this setting for your use-case.
Is there a free option, or otherwise how much will it cost?
When serving models, you will be charged for the full duration that your serving endpoint is active. So, remember to stop your job when you are no longer using the endpoint.
In the near future we will be able to charge users per API call.
And- What should I learn in order to program such a server?
Take a look at this page and use this example as a starting point.
Hope that helps.