As far as the process goes, you would need to set up two Paypal accounts using two email addresses. One would be linked to your Taiwanese bank account (NT) and the other to your US account (USD). To send money, you would login to your Taiwanese Paypal account and send $1000 USD to your US Paypal account. That money (or the equivalent in NT) would then be withdrawn from your Taiwan account and deposited into your US Paypal account. You would then manually withdraw the $1000 USD from your Paypal account, at which point it would be deposited in your US bank account. While the transfer from one Paypal account to another is instant, the deposit to your account usually takes 3 to 5 business days.
Regarding fees, according to Paypal's site
there is no charge if the funds are being withdrawn from a bank account. If you're using a debit / credit card then they will charge 2.9% of the amount plus $0.30, so for $1000 USD that would be $29.30.
I expect they are also making money on the exchange rate from NT to USD.