I want to inquire about fee for Tai Chi course. But, the word "Fee" would not be polite for such martial art. Would there be any alternate word I could use, which is more polite and kind to ask about this.
You could say, "What's the recommended donation/contribution?"
There are definitely instances where the providers of a service do not explicitly ask for a payment; rather, they ask for a donation or contribution, and usually provide a minimum amount.
But, if in this case, the course is advertised with a fee, then you could safely ask what the fee is. The politeness resides in your tone of voice and manner of speaking.