This blue area for

The blue flames are just aesthetic in this particular area. You can't do anything with them.

The 4.4 updated added a new feature that rendered this question de-facto obsolete: now achievement related quests are given an higher priority and can even repeat back-to-back until the player completes said achievement.

If related achievements of a Commission Quest are not unlocked yet, the probability of that Commission Quest appearing will increase.

(source: Official HoyoLab post)

This has the potential to even become 100% if there is a single achievement missing commission under certain circumstances (mostly notable if the player hasn't yet unlocked the other commissions in Inazuma and is therefore only missing the achievement from The Taste of Home in the default pool) causing the same quest to be selected every day until the player finally caves in and gets the achievement.

Obviously this also has the potential to backfire horrendously should the game decide that the player MUST get one of the "You are an horrible person" achievements like killing the pigeons in Timmie quest, locking the player from doing other quests because they refuse to perform some bad actions.