Much like our universe, the story takes place on modern day Earth. However, Magic, and many fantastical beings exist, from the tiniest fae to the most powerful gods.
Much of the events that drove our past have also happened in this one, though with the added 'benefit' of the vast majority of said events having been the result of petty squabbles between the Gods, with everyone else more or less left to try to survive in the aftermath.

With witches, wizards, sorcery, dwarves, vampires, etc, this universe is most definitely a fantasy universe.

Ours, but with all kinds of fantasy beings.

Literally whatever is in our universe exists in this one as well. Some just have augmentations to them due to magic.

The same as in ours, though there exist ways of manipulating and/or utterly defying those laws (see gods and those with the ability to use magic).

Despite magic and technology having existed together since time immemorial, much of the very nature of magic is not understood by those who can't use it. Science has come close several times to imitating magic's abilities, but something always seems to halt it from being the same.

Often, those with magic are given their abilities through blessings of Gods, or contracts with other beings such as devils (or the primordial forces of the universe). Other times, you are simply born with it (fae, elves, dullahan, witches, etc.).

That being said, magic is a rather important thing to the world, in some cases acting as the only deterrent to global annihilation. Whole industries rely on the powers of magi, whole nations having risen through the subjugation of those with abilities, or fallen for the same reasons.

Common enough among humans, it is still a joy to have your child born with the ability to use magic -whereas all elves have the ability to use the arcane arts, humans tend to struggle more to master the same spells, leading to the rise of grimoires.

The exact nature of HOW magic is used is a mystery, even among those who use or have studied it for their entire lives. While some people need to shout incantations for say, Fireball, others can simply think of what they want done and it is done. Even rarer than the unspoken, is the unconscious incantation. Those with this ability usually consider it a curse due to how unpredictable it is. As an example, if your magic were to be sparked by anger, you MAY just end up causing everything around you to burst into flames, or be frozen by ice. Those who have this ability often have spells performed on them at a young age to dull their emotions to such a degree that it is no longer a problem. However, that also has the side effect of dulling their powers significantly as well. Those who are this type of user are extremely unpredictable in their magic types as their emotions trigger the magic itself, lending many philosophers to believe that A) all magicka users are descended from this group, or B) this type of user, while dangerous, is the culmination of centuries of magic evolution.

As for how compatible magic and modern technology is? It's... complicated. Certain types of magic are highly compatible with modern technologies, even going as far as to enhance their functions to a high degree (think an M1 Abrams that now is even more indestructible than it was before), while other things tend to literally blow up around magic users (there's a reason X-ray machines require you to wear something lead lined, and it's not just to prevent possible cancer from the X-rays)...

In regards to the gods, while they are real and they do exert some degree of influence upon the world (read: religions and blessing people with magical abilities or curses), they don't actually do all that much. If they are in human form, its mostly to escape their 'duties' as gods (or in Zeus' case, to pork human women), or to just have fun. In the few times they actively do things, it was mostly in the past when being a god was much more important. Though, most of the time, they only acted to get their worshippers to shut up in one way or another. Just don't ever be an oracle. If the God you associate with is feeling particularly dickish, they may just make one of your doomsday prophecies come true.

Any magic users that are incarcerated have their magic permanently blocked, preventing them from using the full extent of their powers. In some cases, they are given the choice between incarceration, or serving in a magic user battalion in the UN peacekeeping forces.

Some nations still persecute witches and warlocks just for existing. These nations are for the most part not members of the UN, although several member nations DO have severely restrictive laws regarding magic itself.

Similar to the International Declaration of Human rights, there exists a Bill of Rights for magic users, although it has not actually been adopted by the UN. Instead, it is still in the process of being placed before the organization, much to the ire of the magic community.