The ICAO documents contain the complete specification. It is moderately complex and involves twiddling lots of bits. So I've no doubt that a passport reader somewhere isn't doing bounds checking properly.
But you could achieve much the same effect with a hammer.
Yes, but so could a sticker with a QR code containing some exploit that the optical passport reader scans.
I don't think it's a particularly different attack vector just because the chip is "active". Competent systems would treat all data received from it as potentially harmful until proven otherwise.
But you could achieve much the same effect with a hammer.