What is the ruling on that which enters the two passages [urethra and anus]? And does it nullify ablution?

The entry of something into either of the two private parts (front or back) does not invalidate ablution unless it exits. The nullifier of ablution is the exiting substance, not the entering one. So, if a man or a woman inserts something into their front or back private part and it then exits, ablution is nullified, regardless of whether it mixed with anything else or not, and regardless of whether it exited completely or only a part of it; because it is something that has emerged from a private part.