Writing a Letter in Arabic

So I've been taking Arabic for a while, but over the summer I had an Arabic professor who told me to keep in touch-in Arabic, and I realized that I have never learned how to properly write a formal letter. So my questions are:
1. How would you open a letter to a professor? Do you use the عزيزي or is that weird and overly formal?
2. What polite questions should one ask?
3. How do I sign off the letter?
4. Anything else you can think of that might be helpful.
The professor is Muslim and from Jordan if that helps. I want to write it in standard Arabic however. Thanks!

1. you could start الأستاذ الفاضل
2. Inquire about his health, his family's health, say I hope you are doing well, what have you been up to
3. sign off, مع إحترامي // مع تحياتي