Numerous disturbances, including two reported incidents of Israeli civilians shooting at stone-throwing Arabs here, took place in the West Bank today in conjunction with former president Carter's visit to the occupied territory.

According to a witness, the shooting incidents occurred along a main road through Bethlehem about two hours before Carter traveled the same route on his way to a reception held by Mayor Elias Freij.

In the first, three Israelis stopped their car and got out to fire pistols at Arab youths who were pelting the highway with rocks. A short time later, another Israeli civilian vehicle stopped and its driver fired a submachine gun at the Arabs.

No injuries were reported, but Israeli radio said five Israelis were injured in numerous stone-throwing incidents in the Hebron area south of here.

There were also disturbances in the Old City of Jerusalem and at Bethlehem University to mark the Carter visit.

As Carter and his wife, Rosalynn, were touring the Old City more than 100 Arabs marched, shouting slogans and throwing stones. Israeli security forces broke up the demonstration by firing into the air and 13 Arabs were arrested, according to Israeli radio.

Stones and broken bottles thrown by students littered the streets around the walls of Bethlehem University this afternoon after a student strike to protest the Carter-Freij meeting.

Israeli security forces fired several canisters of tear gas into the university grounds during the disturbance but did not enter the campus, where about 1,000 students took part in the demonstration.

Students said they demonstrated to protest Carter's role as the architect of the Camp David peace accords and to make clear that Freij does not represent their views.

"Carter must talk to our representatives, not to Elias Freij," one of them said. "We accept only the PLO Palestine Liberation Organization as our representative."

"Without our organization, the PLO, we will not agree to anything," another student said.

Freij is considered the leading Arab moderate in the West Bank and is the only elected Arab mayor who has not been removed from office by Israeli occupation authorities. His calls for the PLO to recognize Israel and negotiate with the Jewish state and his support for President Reagan's Middle East peace plan, which rules out an independent Palestinian state in the West Bank, have brought him into conflict with more hard-line Palestinian leaders.