Webservice for Android application

  

The tables in the database of my application, to register   user, etc., can be made in MYSQL and hosted on a server and   access the data by the application?

Yes, they can be made without MySQL. In fact the database used for data storage and access on the server side is indifferent; and the decision to choose between one "brand" and another varies according to the need of the project.

  

So, do I need to use SQLite too?

It depends. If you are thinking of developing some mechanism to cache the data captured from the server, SQlite can be very useful.

  

How can different users keep information up to date?

This question is hardly difficult to answer because it is somewhat broad. It depends on your business rules. If your system was a voting system, for example, users would keep the data up to date as they voted. This would give real-time information about who would be winning the vote.

Data generation can be done by the application and stored on a server MySql, PHP, APS, Java, whatever.

You can even save this data so you do not have to make requests to the server every time you need them, but you need to keep them up to date, so do one job only:)