A Few questions on writing a RESTful web service
A bit broad really especially the Python part. 

Yes this can be considered a API. Think of SOAP and REST services as
an API available via the network.
This question is opinion based and not suited for discussion here. A
guideline is that if it works for you it is good.
Yes you should use the REST services for the website otherwise you
will duplicate work.
I just decided to start working on a mobile application for fun, but it will require a back-end.  So I created an EC2 instance on Amazon Web Services, with an Amazon Linux AMI installed.  
I also have set up an database instance as well, and inserted some dummy data in there.
Now, the next step I want to take is to write an RESTful web service that will run on my server that will interface with my database (which is independent from my server)
First question, would this be considered an API?
Second, I am doing research to implement this web service in Python, in your opinion are there better choices?
Third, if I make a website, would/should it also be able to use this RESTful web service to query data from the database?