This can be a stupid question but I am new whatsoever this.
I wish to produce a Home windows program that conveys having a database. Can there be any method of doing this with no user of my program need to use a database program like MySql?
I am likely to program it in C#.
SQL Server Compact matches your needs. However it does not support some benefits. But you don't have to use a seperate database server. It really works embedded.
Because you mention MySQL: MySQL Embedded Database
(It isn't free, though.)