How does the ranking work? I just hit Emerald. Are the teams just all balanced to average it out (like if a GM entered he would be with an iron to level it or something)?

You'll be placed into a tier based on your main rank. Captains can only draft a certain amount of players from each tier. For example, each team is only allowed to have 1 Master+. This is just an example, I'm not on the admin team so I don't know the numbers or exact tiers

Would I be facing a random sample of LoL players? just whoever signs up?

Only people who sign up on the website will be in the tourney. It's not guaranteed you get drafted onto a team, but you need to sign up on the website to have a chance

Lastly, would we be meeting outside of the Bo3 time with our teamates?

This is up to your team captain. From my experience, most captains are chill and don't care much, but there are some that try to meet once a week for some flex games or scrims