Today, I read an article about the Boeing Max 737 planesMax.

Your original sentence wasn't incorrect, but this is a touch more natural. Also, in English it is the 737 Max, not Max 737.

Major airlines have been pulling the Max 737 planes out of737 Max from their flight schedules.

Since the 737 Max has already been established as a type of plane, saying "737 Max planes" is a bit redundant.

Although athe problem with athe flight control system was fixed, another problem withconcerning a microprocessor was discovered.

That new problem with aAccording to Boeing, that new microprocessor problem was fixed, according to Boeing.

However, athe regulatory review process has been prolonged.

The whole Max 737 planes737 Max problems may drag on.

I wonder how airline ticket prices have been affected during this Christmas holiday season.

Major airlines have been pulling the Max 737 planes out offrom their flight schedules.

This sounds more natural to me.

Although athe problem with athe flight control system was fixed, another problem with a microprocessor was discovered.

Thate new problem with athe microprocessor was fixed, according to Boeing.

However, athe regulatory review process has been prolonged.

The whole Max 737 planes problems grounding may drag on for some time.

I wonder how airline ticket prices have been affected in this Christmathis holiday season.

Either "Christmas" or "holiday" is ok.

Although aone problem with a flight control system was fixed, another problem with a microprocessor was discovered.

Your sentence is fine, but I think this sounds more natural.

That new problem with a microprocessor washas been fixed, according to Boeing.

I think "with a microprocessor" is a bit repetitive here.

However, athe regulatory review process has been prolonged.

The whole Max 737 planes problems may drag onProblems may drag on for all Max 737 planes.

I wonder how airline ticket prices have been affected in(during) this Christmas holiday season.