"I hope you're fine" is grammatically correct, but I would avoid it as it sounds awkward and most English speakers wouldn't say it. If you want to sound more natural in your speech, you should not say "I hope you're doing well."

can I text my sir to I hope you are fine

Both forms are correct. The first way is just a more polite way of saying the same thing. I hope you are doing fine, would be a more casual, from friend to friend way of asking the question.

"I hope you are well" is more formal, and is correct. "I hope you are fine" sounds a bit colloquial, though gramatically it is OK.