A respirator is a device designed to protect the wearer from inhaling particulate matter, including airborne microorganisms, fumes, vapors and gases. The correct term for the machine they needed is a ventilator. A medical ventilator is a mechanical ventilator, a machine designed to move breathable air into and out of the lungs, to provide breathing for a patient who is physically unable to breathe, or breathing insufficiently. Calling a ventilator a respirator is a common television and movie mistake.
The farmhouse is well lit and supplied with hot water. Water would likely only be available from a well (that is likely to be on such a remote farm), which would need to be supplied via a pump run by electricity. Lights, water, and hot water are all in plentiful supply.
Fuel and generators are available, the property also has five wells and a large creek. Their power and water came from town before it went down and became overrun with walkers.
The case for running a generator attracting the dead is possible, though some generators for a home run very quietly.
When Rick is standing on the veranda with Hershal (just before Lori arrives), blood is all over his uniform shirt, but there is nothing on his undershirt - if Carl was bleeding that badly, both shirts would have been soaked through.