Can I buy an Easy Card in TPE (and load it with money)? Can I use a credit card for that, or do I need to have NTD in cash to do that?
Yes you can, either from a convenience store within the airport (7Eleven, Family Mart, etc) or from the information desk at the Airport MRT station. The card itself costs NT$100 but comes with no balance, however the cashier can apply balance there and then once the card is purchased.
From memory, credit card wouldn't be an option from the MRT station as you'd need to purchase it from the information desk (they're cash only as far as I remember), but it should be an option from the convenience stores. There's a number of ATMs located around the airport should you need to take cash out.
There's some more information about where you can purchase an Easy Card at the Easy Card website
These standard fare cards cost NT$100 each, exclusive of a deposit and balance.
Four major convenience stores (7-Eleven, FamilyMart, Hi-Life, OK Mart), information centers at Taipei/Taoyuan/Kaohsiung Metro stations, and the EasyCard Corporation Customer Service Center