Are planes allowed to fly in circles, and is there a minimum legal altitude for takeoff and landing?
Most likely there’s a flight school at the nearby airport and they are conducting dual instruction flights over your neighborhood to practice ground reference maneuvers and possibly emergency procedures.  This is perfectly normal and safe.
In the United States, the following requirements for minimum safe altitudes are set for general aviation flight per 14 CFR §91.119:

Except when necessary for takeoff or landing, no person may operate an aircraft below the following altitudes:
(a) Anywhere. An altitude allowing, if a power unit fails, an emergency landing without undue hazard to persons or property on the surface.
(b) Over congested areas. Over any congested area of a city, town, or settlement, or over any open air assembly of persons, an altitude of 1,000 feet above the highest obstacle within a horizontal radius of 2,000 feet of the aircraft.
(c) Over other than congested areas. An altitude of 500 feet above the surface, except over open water or sparsely populated areas. In those cases, the aircraft may not be operated closer than 500 feet to any person, vessel, vehicle, or structure.
(d) Helicopters, powered parachutes, and weight-shift-control aircraft. If the operation is conducted without hazard to persons or property on the surface—
(1) A helicopter may be operated at less than the minimums prescribed in paragraph (b) or (c) of this section, provided each person operating the helicopter complies with any routes or altitudes specifically prescribed for helicopters by the FAA; and
(2) A powered parachute or weight-shift-control aircraft may be operated at less than the minimums prescribed in paragraph (c) of this section.

So unless these guys are dropping below 500 ft AGL, they’re not doing anything unusual.