Using phrases in email to prof (academic)

1. “I hope you are doing well”

Will be it polite, if I write it in an email to Proff/start an email with it?
He was ill, and we wrote me about it

2. Thank you for taking time from your busy schedule to meet with me

How to use this sentense in past tense?

3. I am writing you to let know, that …

“to let know”, is it polite? I woul like to write about what I have decoded according to Proff’ suggestion?

Answer

(1) Yes, that’s OK, or “I hope you are feeling better”.

(2) That’s OK too even if the meeting was in the past.

(3) Nothing impolite about it, but it needs to be to let you know that….

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