How much data will a 64GB memory card hold?

This depends on what kind of photos or movies you are storing, but 64GB will provide much more space than even the average user needs on a regular basis, perhaps in the area of over 4,000 compressed images.

Are all 64GB memory cards the same?

For standard applications like single-shot cameras, it doesn't really matter which class of SD card you buy, as long as it's compatible. However, if you are using this card in a camera to shoot a rapid sequence of photos, you will want to pay attention to card speed.

Can I delete files when the card gets too full to make more room?

Yes, removing photos/videos from the card will free up more space.