1) Are you getting the error in the extension? or is the error occurring on the website?
When copying the API Username, API Signature and API Password values, make sure you are not copying any extra surrounding white space.
Make sure to use the API Username, this is not the same as you account email.
NOTE: The paypal buttons are compiled buttons, they will be complied with the API information you enter.
They will not automatically be updated with live API credentials. when you choose to go live, you will need to recreate the buttons with the live API credentials.
2) The paypal buttons do not work the same as eCart. when using the paypal buttons, the paypal server becomes the cart, not your site. each time they click and add to cart button, they are brought to paypals site, they can chose to continue shopping, or checkout.
The checkout process is done complety on the paypal servers.