They do, but you can't get the card number from reading the chip. The protocol is a challenge-response one based on a private key stored within the chip.
No, you can most certainly get the card number and expiry via the chip and even over contactless, as it’s a vital part of transaction routing/processing. There are Android apps that can do it.
https://en.wikipedia.org/wiki/Chip_Authentication_Program
You need to read the entire card number + cvc2 + expiry date with your camera. That's not skimming, that's just taking a photo of the card.