In the PHP 3.0 SDK there is no getSession() or any session handling from outside the Facebook api available. Some days ago the developers of facebook have also
Well, since everything I did was just a workaround until the new JS SDK comes out, there seems to be no best practice. Setting session.use_trans_sid to 1 and adding the P3P header helped to overcome IE iFrame cookie issues (see my first edit). After a few days of heavy debugging I found out, that FB.ui's permission_request does not send a new access token everytime (<5%).
If this happens, something went wrong. But this little something is driving me crazy. Since this happens infrequently, I can bear redirecting users back to the facebook tab to get a new signed request. With the new JS SDK, hopefully, this won't happen anymore.
There was one little thing I have overseen and the solution can be found here: FB is not defined problem
I did not load the JS SDK asynchronously! This explains everything. Sometimes the all.js file was not loaded fast enough, so there was a JS error. Due to that, neither the permission dialog nor the JS validation worked and an empty #session input value was sent.