Cops can freely buy anything from one of Peter Thiel's panopticon products. He can buy all the data from brokers and companies for a pretty high price, and sell it to cops for an equally stupid price, and your tax dollars get used to bypass the entire concept of a warrant.
No, no need for a warrant. If the cops ask nicely (as opposed to making a demand), and the provider provides the info, there was no need for a warrant. That is the common process today.
Not really, best in class network probes will regularly give you positions that are wrong by a few km, you need quite a bit of cleaning to reconstruct accurate paths.
That's why something like MDT was added to 3GPP standards and emergency calls trigger a hard GPS fix.
Sure, that seems like something that could happen. However, meanwhile, in practice, my friend was having a mental break and the cops narrowed my friend's location down to 3 possible houses in a neighborhood.
Abusing emergency location services is a much better explanation here. They can ping the device for a short time and it'll do its best (using A-GPS and WiFi) to provide an accurate position, without involving anyone since it's fully automated. Collecting positions from a carrier's network infrastructure is a more complex and slow task in comparison.
Towers use sector antennas that can cover typically 15 degrees down to 5 degrees, so the angle from the tower is somewhat known. There are some ways to get an idea how far a device is from the tower with sufficient access, but its usually a moot point because rarely does a device get into a place where it is only being seen on one tower.
