... What? I assume this has to do with her stand and food preparation but what does she mean no gas?

maybe she had a gas stove and it ran out so she needs to use charcoal as backup

Hank Hill would not approve.

Or she likes to make fish with coal, its really delicious that way.

She's being old fashioned.

Just like smoking cigs without filter because it tastes better or something like that.

It's a reference to mitsumoto's Mokou/Mystia strips. In his stuff, Mokou runs a coal-making and delivery business.

...Also, I've recently heard that for grilled eel, you have to use charcoal for it to taste good.

You should always use charcoal if you want your grilling to taste best.