[i]How powerful is an average mage in this world?[/i]
The average mage is fairly weak. They'll specialize in one or two spells, and use some sort of "augment," like a tome or magic crystal, to assist with other spells. Stronger mages can use magic like a natural extension of their bodies and have an intuitive grasp on its principles.

[i]There's a couple of characters with the ability to teleport; is space manipulation a common sort of tech?[/i]
Fairly. The number of people who know the spell is fairly small, and the number of people who can do it naturally is even smaller, but they've made their techniques widely known so anyone can make use of it. Even a novice mage can attempt to copy the spell described in the tomes, and teleportation circles are a fairly common means of transportation.

[i]What exactly are the mechanics of magic (as understood by the natives) in this universe?[/i]
There are several different schools of magic.
[list]
[*]Symbolic: Directly communicates with the world, whether with runes, signs, magic circles, or some other method, to request its obedience. Requires a sacrifice of equal value to the intended effect. Lifeblood is particularly valuable, and the usual method of payment. You'll typically draw a magic circle or inscribe a set of runes and offer a few drops of your blood.
[*]Conjury: Contracts with a spirit to make use of its magic power. These are usually evil spirits (demons), since angels are usually preoccupied elsewhere. You have unlimited use of your familiar's power; you have only to ask (i.e. chant). The hidden cost is often your body, which will eventually fall under the familiar's control if you use enough of their power. If you're lucky enough to find a good spirit to contract with, they'll usually have some sort of stipulation attached to the use of their power.
[*]Thaumaturgy: Uses your natural soul-binding energies (or mana) to exert your will on the world. Can temporarily cause out-of-body experiences; excessive use can cause death. Replenishes either by consuming living matter or by sleeping. This is the most common school of magic.
[/list]

[i]Are we talking about the fairly rigid 'incantation + ritual' combination of more traditional fantasy? Or the more natural superpower-esque stuff from action-fantasy stories?[/i]
That will depend on the school of magic. Conjury (external power) falls into the former, while Thaumaturgy (innate power) resembles the latter.

[i]Do we come in with the sorta general isekai cheat powers that people usually snag?[/i]
Yup, broadly speaking. The reincarnations arrive with greater power than most of the residents of this world.

[i]What sorta religions are prevalent in this world anyhow?[/i]
All kinds. The Zodiac Tribes are largely polytheistic, though they'll focus on one or two patron deities. The outskirts of the Empire is also usually polytheistic, while the inner city folks tend to be monotheistic, believing in either a god or goddess depending on the region. There are even groups here and there who believe modern Earth religions. Since I'm at work at the moment, I can't go into much more detail just yet.

[i]And are the gods real, or just cultural constructs?[/i]
Depends on your perspective, and on the region. Some of the individuals being worshipped are real people with real power; they may be called "gods," but the locals' perception of what godhood entails may not line up with modern earth perceptions of it. Sometimes the deities are purely social constructs derived from higher concepts, with no literal foundation whatsoever.

[i]Also, considering how characters seem to all be major players in some way, do we have control of the NPCs around us, or would the GMs be handling all PC-NPC interactions?[/i]
You know, I hadn't thought about that. I feel like this is going to be a guided story, so for the time being, I think the GMs will be handling all the NPCs. It's a lot of work, though, and player freedom often makes better stories, so that's likely to change in the future.