Whether or not you have a fee for your card itself depends on what card you get; I'm not referring to those kinds of fees.
As for the second point, Mint/Intuit probably covers those fees for their own service, but they don't allow you to interface with them over OFX, so it's a moot point for anyone who wants that information for something other than Mint.
As for the second point, Mint/Intuit probably covers those fees for their own service, but they don't allow you to interface with them over OFX, so it's a moot point for anyone who wants that information for something other than Mint.