I'm working with smart cards in C# using the Subsembly SmartCard API.
Are there any APDU commands(or otherwise) to see either the size of a DF on the card? Or to see a list of the EF contained within a DF?
A DF does not have a size, and may not just consist of files. There is no standardized way of requesting the list of files at the APDU level. To see what's on a file based smart card, the ISO 7816-15 standard is commonly used (which is based on the publicly available PKCS#15 standard).