1. You can access locations via the worldmap where you walk around, not via the overview map on which you build and upgrade constructions.
The overview map has a turn system. You need to use the "end turn" button to advance the turns.
2. On the overview map? Build a lumberjack.
3. Check the paperwork on the desk in your bedroom.
4. Fight vanguard battles. You get equipment and items as rewards for defeating enemies, opening chests, and winning battles.
5. That probably means that you're missing a prior step for Mira's events.