When it comes to the powers of the gods, I may run it with a slightly different twist, even though in practical terms I'm not sure it matters.
Gods don't really gain much power from prayers, they gain the ability to influence and interfere with the mortal realm. In other words, every prayer imparts a tiny bit of divine spell energy to a god. The more power a god gets, the closer they are to the mortal realm and the more influence they have on the mundane world, They can give that power back in the form of spells granted to clerics or other blessings to their followers.
A god that has few or no worshipers may still have residual power which they are only going to hand out sparingly (possibly stored in some artifact or vessel), or could have none at all. If they have none, they no longer have any tie to the mortal world but they do not die. They're still there, they just kind of fade away as far as everyone else is concerned.
In addition, gods of a pantheon will pool their power and give it out to those that are not dedicated to a specific deity. I do that because depending on the region, there are different types of religion. In some regions, humans worship the Norse deities but clerics do not have to be dedicated to a specific deity. In other regions people revere their ancestors. Individual ancestors are not powerful, but they create factions that pool together the power of spells from individual families to grant spells and boons to their worshipers.
In addition, after a period where gods are very active in the mortal realm there will likely be a period where they are very "hands off" until they build up a new reservoir of power. New powers can in theory be created, but in general it would just be an existing entity that now has more direct influence.