Is it possible to display a dropdown selection box with sort options in the frontend for each album?

If you mean if any function or plugin exists, no.

Ok.
Can i do it using Album->sortImageArray( array $images, string $sorttype, string $sortdirection, [bool $mine = NULL] ) ?
$sorttype values are the same of the sort images option in the backend?

Please review the function guide to see what each method produces.