Can agar be melted in oil? This recipe for vegan parmesan apparently has no added liquid apart from melted coconut oil.
Does the agar actually melt and bind in this case?
From https://greenevi.com/vegan-parmesan-sliceable-grateable/
3/4 cup of cashews
3/4 cup of pine nuts
3 tbsp nutritional yeast
4 tbsp refined coconut oil
1 tsp agar agar powder
salt
INSTRUCTIONS
Place cashews and pine nuts in a food processor, and grind until you get a fine crumble.
Heat up coconut oil in a small pot over medium heat. Once it melted, add agar agar and cook for about 5 minutes, whisking constantly.
Add agar agar and coconut oil mixture, nutritional yeast, and a generous amount of salt to ground nuts, and pulse until incorporated.
Place cheese into a mold of your choice (I like to make one out of parchment paper, to resemble a parmesan shape), and press down lightly, if needed. Place in the fridge for at least 4 hours to let it set.
Cheese will keep for 7-10 days in the fridge. Enjoy!
Here is the molecular chemical structure of agar.
https://en.wikipedia.org/wiki/Agar#Composition

It is a polysaccharide and like all polysaccharides will be strongly hydrophilic.  To answer the question: there is no way a molecule like this will dissolve in oil.  You might be able to make an emulsion but you would need an emulsifier and there is none I recognize in this recipe.
As regards the larger question of why this recipe calls for agar I do not know.