Interaction between role selection, role popularity, role assigment and queue times?

I have some questions about the interaction of role selection, role popularity, role assigment and queue time in the new champion selection.

You can select two roles in the new champion selection. How much more likely is it to get the primary role than the secondary role? 67%:33% maybe or 75%:25%?

How much is this affected by the overall role popularity?

Lets assume some roles are more popular than others. Just as example to calculated with: Mid: 26.66%, Top/Bot/Jungle: 20%, Support: 13.33%. (Mid twice as popular than support)

Lets asssume it is overall twice as likely to get the primary than the secondary role. If I now choose mid primary, and support secondary, is it still twice as likely for me to get mid than support with the doubled queue time, or is it a 50%:50% chance to get mid and support with average queue time?

And how does fill work? Does it ensure that I get every role equally often over a long period of time with average queue times or does it give me unpopular roles systematically more often than popular roles with lower queue times than the average?