Why would Freya be so focused on a low-level adventurer, wanting him to grow stronger as his ability helps with and having 'tests' of his skill done? Freya's not only a goddess of beauty, in the original mythos. Her domain also encompasses war and death.
When does Bell receive the Argonaut/Hero's Wish skill? After he had found and discarded his grandfather's dream for his own of being a hero. His grandfather told him to rescue a weak female adventurer to start a Rescue Romance and Bell had already done so with Lili. If he still believed in his grandfather's words then he could settle down with her, mission accomplished. Thanks to his experiences in the dungeon however, Bell has a new dream and yearns to become a true hero instead.
Why Hestia has a hard time recruiting members, in spite of her central position in Greek mythology? It would be more reasonable if you know Familia members are supposed to further the Gods' domain... Hestia's domain is in the hearth and the family, which, while important, is hard to recruit employees due to What Kind of Lame Power Is Heart, Anyway?.
Sounds like it would make her the best person in Orario to run a hotel/B&B chain. Possible future career for Hestia once she's worked off the cost of Bell's knife in Hephaestus' store?
Why is Bell a Chick Magnet? Well for one he probably has the blessing of Zeus who was masquerading as his grandfather.
Hestia and Hephaestus have been BFF's since long before they came to Earth. Why? Might have something to do with Hestia being the Goddess of the Hearth - which contains and supports any fire. As a blacksmith, Hephaestus is dependent most of all upon a reliable and safely contained fire... which requires a good hearth.
Bell's magic being named Firebolt makes sense when considering whose Familia he is a part of, as well as his own family. Fire is a reference to Hestia as she is associated with hearths while bolt makes sense because prior to meeting Hestia he was Zeus' adoptive grandson.
It's been established that Bell's grandfather was a bit of a pervert and Dirty Old Man. However, once it's revealed that Bell's grandfather was actually Zeus himself, a renowned womanizer, it actually makes much more sense and is appropriately fitting for Bell's grandpa to be the way that he is.
Much like Bell's magic making sense when considering the main influences in his life at that point, so does Welf's. His Anti-Magic spell not only represents his antipathy for his own ability to forge magical weapons, the fact that it causes a Magic Misfire that damages the caster represents how the loss of that ability caused the downfall and ruin of the Crozzo family. Even it's name "Will o' the Wisp" makes a lot of sense since the ability to make magic weapons comes from one of their ancestors essentially became Blood Brothers with a spirit.
The Reveal that Dionysus really is Enyo makes sense. Dionysus is the god of wine and madness.
Those who read Aiz's side story will know that on the lower floors, there is at least one species of monster that hunts other monsters. Monsters have been known to flee UP the stairs when threatened. (It's the reason Bell met a Minotaur on the fifth floor.) Monsters don't communicate and are always immediately hostile to any human they come across unless enchanted otherwise. And lastly, Monsters spawn, fully formed from the dungeon walls, endlessly. If it wasn't for the efforts of adventurers to keep monster populations in check, it would only be a matter of time before high-level monsters swarm out of the entrance.
This is in fact confirmed later on in the novel. The world was overflowing with monsters from whatever the hell is now at the bottom of the dungeon, and there was no way for humans to fight back. Then the Gods came down, slammed the dungeon on top of the monster-spawning pit, and gave humans the power to fight back against the monsters.
Aiz is 16 years old, and a ten-year veteran of the dungeon. While normal girls were in kindergarten, she was stabbing goblins. A lot of goblins.
Even the lowliest adventurer is supernaturally strong and regularly kill monsters almost as big as they are. An experienced adventurer is capable of throwing around ten foot tall monstrosities who can break apart rock walls with their bare hands. We already see examples of adventurers extorting and murdering each other in the dungeon; what's stopping them from turning on regular townsfolk they don't like?
The light novel elaborates on this issue. The Guild also acts as Orario's government and has several tools to control Adventurer behaviour; for example being struck off from the Guild's list of Adventurers due to on-Earth mishaps also forbids said Earthlings from selling Magic Stones. This is why any illegal behaviour among Adventurers must be inside the Dungeon as the Guild's laws don't apply there.
This is what happened to Lyu, her Familia was ambushed and murdered inside the Dungeon, she took it outside the Dungeon, which is why such a badass level 4 adventurer like herself is working in a kitchen.
Soma Familia in general. Soma really doesn't care much about the members of his Familia, and only wants them to bring in money to finance his true hobby. Those who meet their monetary quota are given samples of his wine, of which even the dripping and rejects are so good as to be addictive. For most customers, the price and demand means that the short-lived addiction will wear off long before they get another taste. But for members of the Soma Familia, the next taste can come as soon as tomorrow, if they get the money. Which pretty much makes a good portion of the Familia a gang of well-armed addicts willing to go to great lengths to buy their next fix.
Not pretty much - more like absolutely. If you read carefully, Lily strongly implies that because her parents were part of the Soma Familia, she wasn't born into membership but indentured servitude. In Volume 6, she's implied to be pretty much the first person ever to actually overcome the effects of Soma's wine - rather than having it wear off - by sheer willpower. It impresses Soma so much that he not only lets her leave the Guild, it profoundly changes his attitudes towards his children and how he treats them.