I think I'm still not used to this way of tleachrning in person, because I feel very nervous and embarrassed.

This way makes it clear that you weren’t the teacher, though the way you had it is also correct.

In which I think mythe pressure will be less that way because I know the teachers are far away from me.

“In which” would need to be after a comma rather than a full stop. Also we say “the pressure” rather than “my pressure,” I think because it’s the pressure of the situation rather than something that comes from you.

I hope you progress in your studies, and wish you health and, happiness, and a bright future.

“I hope you health and happiness” would be wrong, so we have to tweak the sentence a bit.

I still want to take my original online class, in which I think the pressure will be less because I know the teachers are far away from me.

This sentence needs to be connected with the next one, because "in which" is a preposition.

I hope you progress in your studies, have good health and happiness, and a bright future.

The verb "progress" only makes sense for the teacher's studies. For the rest, you can just say that you hope the teacher has good health and happiness, and a bright future.