1) You can save all these in your self file-format or you can use sql,xml etc.
Point here is if your game is an online game or a single player game. For a single player game saving data on a remote server is not really a good solution, nor running a server on user's machine.

2) If you really need to use SQL, use one of the libraries that do not require a server to be running, like SQLite or MS Access.

3) you need plugins to use a SQL server, connection string is more like .net thing, f.i. in MySQL or SQLite you do not use connection strings. For MySQL you pass your server's ip,username and password to a function then you select a db with another function. For SQLite you only need a filename, there is no server to connect to.

There are other things to consider when using a SQL server from your games. First, a note, I am going to name game's main executable where players run to play the game as "Client". You do not want to directly connect to your database or db/server from your client. If you do that you have to provide your username/pass/connection string either in your code, hard-coded, or in a config file which is not really healthy for your server's security. If a local database on the player's machine is sufficient for your needs, use SQLite. SQL syntax is not much different from MSSQL. If not, you need a "game server" for your problem. The function of the game server is to get data from clients and connect to database then store that data there. This way you can validate the incoming data on game server and do not expose your database credentials in your cliet.