Gods usually do whatever they want, though they may be drawn to things similar to their divinities. Ex: a god/goddess of smithing may get more enjoyment out of life when they are smithing, though that wouldn't be the only thing they would enjoy.
Gods could do one of three things: live on the planet, live in the divine realm, or do nothing. Ex: dunmachi, regular fantasy, worlds where the gods can't interfere.
Gods would be able to speak in a universal language so that no misunderstanding occurs. Meaning that when they speak than anyone would hear it in the language that they are most familiar with and in such a way that each individual would be able to understand. It expresses the meaning in words in such a way that everyone would be able to understand.
The reason why the god's language is named as such is that usually, only the gods can use it. It requires a complete understanding of the rune, what it represents, how it reacts to everything else, and the exact opposite of the rune. A basic ex would be the rune for fire; one would have to such an in-depth understanding that it would be impossible, usually due to magical/technology level and time, for someone to understand truly. So if someone used a fire rune in the god's language, then it would be like a sun appeared on the planet while an ice age happens around the area.
Gods usually need faith from their followers to do anything in the physical world, though this depends on the god's circumstance.
ex:
1.) for a world like dunmachi, the gods walk the earth with you. This would let the gods get faith a lot easier, but since they are on the planet, they are limited in what they can do. Keep in mind that even if you do kill the god's mortal shell, the god would still live, it would just take some time before they descend again. This situation usually becomes a give and take relationship. In this type of situation, there are usually less holy/unholy wars; there is still war, just usually not of the divine kind.
2.) for a regular fantasy world, the gods are either in the divine plane or in their respective pocket dimension. This is where the gods are usually divided and have holy/unholy crusades to weaken the other gods' power while increasing their own.
3.) Worlds where the gods can't interfere. In this type of situation, the gods are usually heavily restricted and usually can't go down to the physical plane in a convenient matter. These types of gods usually only talk to their most devout followers. Any war by the church are usually not instigated by the gods, but instead by the head priests.
Each race would have there unique types of benefits. A siren would have an easier time learning a chant for a spell, but I believe the spells that they would best at are an illusion, wind, water, and sound type spells. In other words, they would more than likely have an affinity for them, though there is always an exception, like for ex: they could have an affinity for fire, earth, or whatever.
In my opinion, medusas petrifaction is a passive skill mixed with a curse. It is always on and will affect anyone that doesn't have the proper defense or resistance. The skill only works when you look into her eyes, so if you bring a blindfold or wear contacts, then nothing would happen. You could wear glasses, but it would depend on how bad the person's eyesight is. Your eyesight could be so bad that the skill wouldn't be effective because you aren't looking ar her even if you look directly ar her.
Note: gods are only restricted by gods, usually by a more powerful group of gods. Though it would be like in dunmachi, where everyone would have a say and the powerful neutral god would say the final verdict. This is usually the case of too much power. They usually restrict the use of the god's language in the physical plane, but they can use it whenever in the divine plane. when they do use the god's language in the physical realm, it's power is usually restricted to prevent unneeded destruction.