Location sharing

Read Find people and share your location with Find My - Apple Support to find how it works.

It's accurate to within most people's definition of the word.

The green pulsing bubble indicates a live reporting of the location on the map.

I haven't seen the bubble move without the located person's image, so I can't answer that.

An Apple Community Specialist answered many of these questions with a high level of detail and I refer you to that response in this thread.

Improve GPS accuracy

GPS accuracy depends on the number of visible GPS satellites. Locating all visible satellites can take several minutes, with accuracy gradually increasing over time. To improve GPS accuracy:

• Make sure that you've set the date, time, and time zone correctly on the device in Settings > General > Date & Time. If possible, use Set Automatically.
• Keep a clear view in several directions. Walls, vehicle roofs, tall buildings, mountains, and other obstructions can block line of sight to GPS satellites. When this happens, your device uses Wi-Fi or cellular networks to determine your position until the GPS satellites are visible again.

About privacy and Location Services in iOS and iPadOS - Apple Support (IN)