What is the correct medical procedure(s) for taking a resting heart rate?
1) According to this article you should be taking it in the most preferred position you want. It would change according to the position you are in so make yourself comfortable sitting or lying down (reference).

2) You take the number of beats of your heart in a minute. If you take the number of beats for 2 minutes, then average your count by 2. 

3) One minute (reference). 

4) Completely relaxed, most articles recommend taking it in the morning while waking up so you are doing the right thing (reference). 

I don't understand what you mean by an academic situation so I could try and answer it if you clarified it.