

Your ip is the identity of your router.
By using simple tools you can find the manufacturer of your router and potentially use a known security to gain access to your network.
You expose yourself to being targeted by focused network attacks, since they know the address belongs to you.
In ye olden days, it would have been possible to track your ip and what it was accessing online. Its harder to do today due to cryptography and vpn’s, but still a risk.
No, of course not the MAC. Just as an example nmap can guess the OS based on fingerprinted behaviours. There are pentesttools that can guess the OS.
Like i said. Old days. You could get access to a distribution switch where the physical security was all that mattered. The town where i grew up had some early variation of cg-nat that meant all devices where in a way on the same network. It created plenty of issues when trying to play online with friends during Quake/WC3 etc.