How should I call my professor?
I have to write to my professor, but should I call him by his first name or last name?
Also, except for Hello and Hi, what else words would be more polite and appropriate to use when writing to the professors?
For the ending, what other words or phrases are preferred except for Best, and Sincerely?
Thanks!

Question

How should I call my professor?
I have to write to my professor, but should I call him by his first name or last name? 
Also, except for Hello and Hi, what else words would be more polite and appropriate to use when writing to the professors?
For the ending, what other words or phrases are preferred except for Best, and Sincerely?
Thanks!

Answer

Write in a formal manner.

Date
Dear Professor. XXXXX/ Dr ......................,
I wish to ask you about ............................
Yours sincerely,
Your name and surname.

Answer

1) usually it`s "professor + last name" 
2) Hello is polite enough, unless you want to make it *very* formal - in that case Good Morning/Day/Evening works best
3) Yours Fathfuly? Yours Truly?

Answer

Unless told otherwise by your professor, you should definitely use last name with a title, either "Professor Lastname:" or "Dr. Lastname:" if Dr. is appropriate.

No other introductory word is necessary, just place the colon after the last name.

In the USA, "Sincerely" is the standard closing for a formal or semi-formal letter. "Best regards," or "With regards," are also fairly standard.