Do you have to wait after eating dairy before eating meat? And what changes with hard cheese like parmesan?

The Shulchan Aruch (Yoreh Deah 89:2) says after cheese a person can eat meat right away, just check the hands and clean and rinse the mouth, and for chicken not even that. The Rema adds the custom of not eating even chicken after hard cheese, like waiting after meat before cheese, brings the Zohar, and says it is good to be strict.

1. After regular dairy, milk, soft cheese, ice cream, is there any waiting at all before meat, or is cleaning the mouth really it? Where does the common half hour or hour wait come from?

2. What makes a cheese “hard” for this, and does parmesan count? Nobody seems to wait after parmesan on pasta.

3. Is waiting after hard cheese a flexible minhag like waiting after meat, or stricter because of the Rema and the Zohar?

4. Bottom line: after dairy, what does a person actually have to do before meat or chicken?

Basically, what is the source for waiting after dairy before meat, and where is the hard cheese line?