Your doctor will need to give you the specific answer to each of your questions.
People using oxygen continuously for COPD are able to travel by plane. Since you need oxygen for sleeping, your oxygen level may be low in Ohio. A plane is pressurized so that it is about the same as 8,000 feet in altitude. If your oxygen level is low in Ohio, which is close to sea level, you will probably need oxygen during your flight. With the amount of oxygen that your doctor recommends during your flight, there will be no risk from your pulmonary hypertension. When you make your reservations inform the airline(s) of your oxygen need. Some airlines do not provide oxygen. So you may need to find one that does. The airline will let you know what they require so that they can provide you with oxygen during your flight. Usually they will need a letter and a prescription for the oxygen from your doctor. No airline allows anyone to bring their own oxygen on any flight. If your travel to Santa Fe will include any airport layovers, an oxygen company close to that airport will need to supply your oxygen. Check with your oxygen company at home to have these arrangements made in advance. The airline only provides oxygen on the plane. They do not supply the oxygen in between flights.
Since Santa Fe is at an altitude of 7500 feet you may need to use oxygen continuously during your stay. Your doctor will need to determine your need for oxygen and the amount of oxygen.
Ohio mean elevation is 850 feet above sea level, while Santa Fe's elevation is 7,040 feet.
I have moderate to severe emphysema. I do NOT need any supplemental oxygen at sea level (where I live in Hawaii). At 5000 feet (in Denver), I need supplemental O2 @ 2 liters/minute for exertion and sleep. I do not yet need O2 to fly, as long as I move slowly and stay awake (I keep my saturation rate at or above 90%).
I would suspect that since you already need supplemental O2 to sleep in Ohio, you would need substantially more for flying and in Santa Fe. You can ask your doctors to evaluate you and make recommendations about your needs.
You are correct that currently all oxygen for airplanes must be arranged by contacting the air carrier and paying for them to get any oxygen, if they allow supplemental oxygen aboard their planes. Airlines charge fees for this service, which can be based on the number of tanks you use or the number of legs you travel. Each airline sets its own criteria and prices.
Another option is to travel by car or train, which would have the advantage of allowing you to bring your O2 supplies. Your local O2 supplier should be able to help you with arrangements for your trip and destination.
You would need to ask your doctors about cardiac risks of flying and altitude as well. Many COPD patients find altitudes difficult to tolerate, especially when it increases their supplemental oxygen needs.
Starion