Trying to create a custom league, I see the tab for league structure but it is greyed out. I am in the beginning before the draft. How can I access this option?

This is done via mods of the teams.xml file when you create a league: viewforum.php?f=285

The league structure unlocks between seasons if you wish to change league formats (expand, contract, etc.) but only allows team formats that are already available in the game.

Can you move teams from one division/conference to another between seasons?

yes