What exactly are these things and where do they come from? And how?
Well it says in the name that they're spirits so they could be spirits from the spirit realm. Would make sense since they also reward us with charms.
We've seen a creature emerge from bonfires in another instance as well. Fallen Nihil at the Lumbridge Crater.
Fallen Nihil: "My Queen noticed this world appear in the heavens as if it had been revealed from behind a curtain. Last year she felt an increase in fire energy in this location. She had her pyradins spend a year preparing to use that energy. With it, she could bring me through the planes, in the hopes that the energy would build up once more."
This shows us that interplanar travel is possible by using concentrated fire.
So I think the Fire spirits use the same method of transport as the Fallen Nihil did. They're smaller, weaker and probably closer by than Fallen Nihil was. Therefore not requiring as big of a bonfire as he did. Perhaps they also have natural ability to travel this way and that's why they don't need these "pyradins". Or it could even be that these (or beings like them) are actually these pyradins, using their powers to allow others travel the way they do.
It does say when they're released that they're released from the logs. But this could be just meaning that the logs by burning are releasing them or something and they aren't actually trapped in the logs? Why would a fire spirit be trapped in logs in the first place?
Flame gloves and Ring of Fire can attract them too. Perhaps they simply add to the energy of the fire or help focus it or whatever?
...
Fire burns through lies and illuminates darkness. It rains destruction upon enemies and brings warmth to friends.