> Can I start Firebird Embedded from Java and connect to it?

Yes. In fact you have simply to copy files from FB Embedded to your
application directory (not only fbembed.dll) and set the FIREBIRD env.
variable to point to your application directory. Also you have to ensure
that jaybirdXX.dll (current version is jaybird21.dll) is in the
java.library.path (by default on Win32 it is equivalent to %PATH%) and
fbembed.dll is in the PATH, so ensure that PATH includes either your
application directory or %FIREBIRD% variable.

> If so, how can I do it and what is the connection string?

Simply use the jdbc:firebirdsql:embedded:<path to database> URL.

Roman