Granblue fantasy

Well, I was clearing the free daily quests because I wasn't sure if they accumulated.

They don't accumulate. But you don't necessarily have to do them at 11 PM; you can time it so you do them at 1 PM if the next period is expected to be more beneficial. That's what I did.

Let Ment confirm if that's the case.

1) I don't have Lucy, so I don't know. You can check the wiki.
2) Even if I did have Lucy, I'm already playing through the second Sky Dome. I probably wouldn't have any problems with quest blocking.