The free version includes pretty much everything (dungeons, exploring, shop, etc). The affection system is the majority of the premium update, and the rest is a long list of quality of life improvements and bug fixes.
The shop opens at or around day 150 (the girls will talk about it). The default is for the girls to take you together, but if you're on Lani's solo route, Lani will take you alone. After you've been to the shop, it will appear on your map (but it's not currently a fully functioning shop).
