In a database mirroring if the failover occurs, how application will automatically connect to the failover partner? Is their any setting from the database server end to achieve this?

Connection string is:  

string cs = 

Data Source=myServerAddress;

Failover Partner=myMirrorServerAddress;

Initial Catalog=myDataBase;

Integrated Security=True;

Can we configure mirroring between Standard Edition & Enterprise Edition or Vice Versa?

Nope, its not possible, both principal and mirror should have the same edition.

Does mirroring support FILESTREAM file group?

NO. Database mirroring cannot be configured for a database that contains FILESTREAM filegroups.