Can a phone be tracked without a sim card, especially with the involvement of authorities like the police?

To know the answer of - can a phone be tracked without a sim card, you must understand that a SIM identifies you with your network operator; it is necessary to be able to receive calls and to bill you for calls you make. Without a SIM, a phone is mostly useless as a phone, but it can still make emergency calls (in most countries). Without a SIM, your cell phone will not normally transmit data to local base stations, but if you make an emergency call, it will identify itself with the cell tower by sending its IMEI. So there is some information identifying your phone that can travel on the cell phone network, but only at your own behest. I don't know how easily the police can access this information. If you've turned off GSM altogether and are only connected through wifi, it's a different matter. The wifi access point knows your phone's MAC address. Whether (or how easily) the police has access to that depends on who owns the access point.

Beyond that, your internet traffic does not inherently contain information that identifies your phone, but there is a lot of indirect information. Your IP address will pinpoint at least the access point's ISP and your general location, and with the cooperation of the access point owner your access can be tracked back to the access point by someone who is trying to trace your traffic. The content of your traffic may or may not identify you or your phone, for example through browser fingerprinting, or simply because you logged in to some online account. If someone is in the vicinity of the access point, they can physically locate your phone by measuring its radio signal.