Based on the fatawa of Ayatullah Sistani:
If a person performs prayers in a place where people pass-by, or, if someone is in front of him, it is recommended that he places something in front of him; and it is sufficient if that thing is some wood or rope. A tasbeeh could also be used to show one is praying in this area.
Prayers are not invalidated by the passing in front by other persons. It is not makruh to pass in front of a praying person
As for the walking on the haram floor with shoes from the wudhu and washrooms, if this results in desecration of the or najasat of the mosque then it is haram, otherwise not.