Convert C# single-user application with MySQL DB to multiuser application

Question

I am experienced enough with single user desktop application in C# with MySQL. Now, I have a requirement to develop a mulituser desktop application with MySQL. I need to know a few things here:
 - Given that i am using MySQL DB, do i need to programmatically take care of data corruption/integrity /locking issues in my code in multi-user environment?
 - When the application is ready, I will create setup project of my app using Visual Studio. My question is: will the server only have database & the client application will be installed on all computers? Is that correct? All the client software will use the central database residing on a different location.
 - How do i create Visual studio setup project to create the MySQL database on the central location?

Is there anything else I need to take care in a multi-user environment?

Please advise!