I'm sure there are others here that can answer this better than I can, so please correct me if I'm wrong.
Well it somewhat depends on if you are planning to sink any money into this game. From an F2P standpoint, Hanuman > Leviathan >> Nidhoggr > Cereberus. If you are planning to spend a bit, then I'm not sure it matters as much. It's mostly just preference.
Sort of. Light is currently one of the stronger elements despite not having a 140% eidolon because of its insane kamihime synergy (Lugh - Tish - Iris - Mike). It also benefits from having no weaknesses, meaning that you can hard focus on light without any issues. However, I'm not sure if I would consider a Managarmr + core SSR reroll to be "better" because I feel that you need the kami synergy to make it on par with a 140% eido + core SSR reroll. Although I'm not a light main, so take it with a grain of salt.
Yeah, dark right now currently feels a bit underpowered right now (sorry Yukarichan ). However, with additions like Nefertem and Thanatos AW, dark will be getting quite a bit stronger in the future. So I guess it depends on if you are willing to wait until dark gets stronger and if you are willing to mtix those stronger kamis once they are released.
This is a quick list that I compiled of core kamis that are currently in the gacha pool...
(loosely ordered)
Fire: Fire Frey, Vahagn, Svarog, Fire Mammon, Uriel, BFM Amon
Water: Cthulhu, Vohu Manah, Shiva
Wind: Azazel, Cybele U, Cu Chulann, Gaia/Frigg
Thunder: Baal U, Dian Cecht, Raiko, Marduk
Light: Michael, Iris, Tishtrya, Lugh, Eros
Dark: Nefertem, Satan, Susanoo, Amon U
There isn't really a specific formula or method to show if a kami is strong or not. It's more of something that you can pick up on as you start to test what abilities work well and what abilities are trash. Generally speaking though, any kamihime with a 30% elemental resist debuff is generally core. Other than that though, it's difficult to say.