Hello and welcome to Advanced Installer forums,
Since you want to connect to an SQL Server, I would suggest using our predefined dialog "SqlServerConnetionDlg". This is a dialog which is specially designed to be used with SQL Server and it pretty much does everything for you (e.g. it creates the connection string, establishes the connection to the server/databse, etc.). After adding this dialog, you can see all the changes in the "SQL Databases" page.
In what regards your second question, you can go to "SQL Databases" page --> select your database server --> check the "Trusted Connection (Windows Integrated authentication)" option.
Hope this helps.
Best regards,
Catalin