Yes but. Safe is not the problem, your personal comfort may be a problem. If you are ok for a car, then you are ok for an airplane.
Yes. Yes, it is ok to travel by airplane until your last month of pregnancy, when it is wiser to curtail long distance travel regardless of mode. You should travel with a copy of your prenatal record and your physician's contact information. If you have been advised due to a high risk condition to not travel/fly, or you have a specific concern about your pregnancy, defer to your doctor's advice.
Yes. But it depends on where and how far along you are. You don't want to be in a place that can't take care of you and the baby if an emergency arises. Also you really want to be close to home in your last month of pregnancy.
Yes. In an uneventful pregancy, there is no problem with traveling on an airplane. If it is a long flight, you should get up every hour to strecth your leg muscles to help prevent a blood clot, which is a rare complication.
Yes. Airplane travel is safe during pregnancy due to pressurization of the cabin, etc. The real issue is two-fold: making sure to get up and walk around every hour to avoid "stasis" of blood in the legs (risk of blood clotting) as well as emptying your bladder; and, after a certain gestational age (usually 28 weeks), how far do you really want to be away from your ob/gyn if something does happen?
Yes. In an uncomplicated pregnancy, it is generally safe to travel up until about the last month. Travel above 10, 000 ft in an unpressurized cabin can cause problems with the placenta. Sitting for prolonged periods in an airplane can increase your risk of blood clots in your legs so getting up every 2 hours is important.