Vito referred to Sollozzo as an infidel because Sollozzo was known as the Turk because he had a wife and kids in Turkey. Since Turks are Muslim and Vito was Catholic (nominally), Vito referred to him as an infidel because that sometimes is one way, though a pejorative way, to refer to someone of another religion especially when that other religion as been something of a political or military opponent of your religion (the Crusades, for example).

As far as other gangs moving in on Mafia territory goes, it depends. The Westies in Manhattan caused havoc in that area of New York much of the time on Gambino family territory. Eventually, Paul Castellano as head of the Gambino family at the time made a deal with the Westies that permitted them to use his name and operate in that part of Mnhattan as long as they paid for the priviledge. The Mafia is not omnipotent. Today, they have to struggle in some cities against other ethnic gangs for their share of the pie. But, they have learned that cooperation is more profitable than the spilling of blood.