I read datasheet so that Q1 and Q2 answer is yes. As clock connection is listed as separate point in addition to setting remote loopback register, we can conclude that it's not achieved just by software.
Other PHY chips like LAN8742 are enabling remote loopback by just setting a bit, so neccessity of external connection for KSZ9131 is probably a silicon bug or something that the designers couldn't make easily software configurable.