How brief I should be when contacting a professor for a PhD position for the first time?
Professors receive a number of such emails. You must get the professor's interest in the opening few lines.

"I am a prize-winning A+ student in the department of X at the university of Y. My most recent work - my honours study of 
Z - is very relevant to the advertised PhD position. I am very keen to talk to you about this opportunity, by email, phone or Skype, whenever would be convenient with you".

And then by all means ask your questions, that is good, it shows engagement. You could also expand on why your previous work and/or skills will be valuable to the professor.

You could get another professor to proof read your email to see if it hits the right note.