Good question, as I recently looked into this myself.

My understanding is the EasyCard does NOT work with Apple Wallet due to various technical and commercial reasons (the best article I found is here, in Chinese: https://www.bnext.com.tw/article/721...percard-2022q4)

As for recharging, I've only used cash, but my suggestion is to try at 7-11 and use a credit card.

And lastly I believe the card will work in Kaohsiung. I've never tried myself, but I've seen Youtube videos.