Your theme extends a core WordPress class with its own fs_connect function, but doesn’t accept the same parameters, which is why it’s causing a “should be compatible” error.
This could be caused by WordPress updating it’s WP_Upgrader class, in which case your theme will need to update to be compatible. Or, more likely, this website is running PHP with different error reporting settings. This error probably isn’t breaking anything, so some settings will hide the error.
Another possibility is running a different PHP version. In PHP 7, for example, the “should be compatible” error no longer requires “strict” error reporting to appear.
Ultimately it’s something your theme’s developer would need to fix (it should be trivial), so you should report it to them.
The other two errors are just being caused by that first error appearing. Errors that appear at certain points in the page load can interfere with headers, which will cause those errors. Fix the first error and they’ll go away.