I've played sandbox for an hour now. Yes quests are here too, which is weird.
Also I haven't tried yet to reach the second Era without quests but it seems rather complicated to do so, as you need specific requirement and quests help you on that front.
Otherwise some of them will still pop as a exclamation mark and can be ignored as in tropico 4.
But for now I'll agree that I'm super confused about how the mechanics work and the tutorial didn't help me either, while in Tropico 4 I knew what I was doing and the game explained it rather well. I4ll see if the campaign can fix that but it looks like the game is designed that way.
Overall I just want to go back to 4 for now. My worst fears became true D:
I don't like a lot of the changes they made, and the game feels awfully different yet still the same. OST is a downgrade too. I don't like having a research tree, I don't like having to switch eras to to anything worth my time, I don't like being locked out of any useful building until I reach the next Era, I don't like the fog of war, I don't like dynasties, I don't like the fact I can't control my Presidente anymore, blah blah blah.
Colonial Era especially feels so pointless it's not even funny.
Most of the changes feel like useless artificial barriers to me and worse, feel designed to accomodate multiplayer.