Does Egypt have the ability to interfere in its allies affairs? No, they are sovereign nations that make their own decisions. Decisions that the current Egyptian regime does not support.
No, apart from the Urban areas and their surroundings in Northern Sinai which is the area that ABM/SP is predominantly active and contained (i.e Elshiekh Zewaid and Rafah) it is incredibly hard to police the movement of people due to the nature of the areas topography and its size.
You simply can not send patrols of any kind into the desert to search for thin air. Losses will happen, they already have, that's a given. But in the end they haven't made a dent in three years, a few armoured vehicles, second generation tanks, patrol craft, and a few hundred personnel are nothing in relation to the size of the Egyptian Armed Forces and the sheer manpower it can bring to the fore.
ABM/SP are fighting a losing game regardless of the Egyptian Armed Forces' frailties when it comes to asymmetric warfare/COIN.