Those are blessings. You need to collect 4 blessings in order to continue the main story line (To reach ED 1). You also need to do a lot of substory quests involving the main characters / Heriole.
Here is the full save findable on the japanese net.
There is a walkthrough out in Japanese for this game (and definitely would recommend using it if you want to continue the scenarios. It would be a bitch to figure out where to go sometimes, since it's basically open-world with scenarios). Note that completing the main quest without doing side quests results in a bad end where you fight against Eliza.
You must be registered to see the links
You might want to wait for a translation before doing the scenario? It was decently enjoyable to read, mostly because I enjoyed the way Heriole talked. The MC doesn't say very much, but basically Heriole will teach you a lot about the world / history in his ramblings. The text is not very straight forward / blunt, so I don't know how well hooks/translations will work.
Main scenario / Vampire scenario were interesting/fun enough to follow, Vampire one is definitely the toughest fight in the game. (Harder than the last battle in main scenario imo)
Eremia scenario was pretty mysterious and interesting, but at the same time I wish there was a little more to it. It wraps up nicely enough, but it feels like more could've been done with it.
I'm not sure if Rita's story has any connection the main storyline, I followed the walkthrough and it kind of did Rita's at the same time as it went through the main storyline. She doesn't really show up in any of the main scenario events though.
Kurumi's event is simple enough, and needs to be completed to finish upgrading your weapon. She's the strongest partner you ever pair with for sure.
Romenia ending was pretty lackluster. Maybe development in the future?