1. Why would a drain clog at one end of the house cause gurgling air bubbles in drains at other ends of the house? Bathroom 2 is the furthest from the street, the other drains are between bathroom 2 and the street.
2. Was the problem really resolved, or is this a symptom of a whole-house sewer drain problem caused by things such as tree roots?
1. It shouldn't.
"Gurgling" and all of your other symptoms usually indicate a clogged vent stack, not a sewer line problem.
When you flush a toilet or run water down a drain, it creates a vacuum inside the pipes. The system is supposed to be designed so there is a vent pipe that allows air in behind the draining water to fill that vacuum. If the vent is clogged, the system will try to draw in air from wherever it can and, since all of the plumbing is tied together. if the vent is clogged and the system can't draw air in through it, it will draw in air through the other drains in the house. That gurgling noise is air being drawn in through the traps in those other drains (your toilet has a trap built into it as well).
If the system can't draw in enough air, that vacuum can be strong enough to pull raw sewage back up through the sewer system. And that's why you get toilets backing up.
There should be a vent stack (usually a 1.5" - 2" pipe) coming out through the roof of your house or running up the side of your house to the roof line. Check it and make sure no animals have moved in or that it hasn't become clogged with debris. On occasion a squirrel, a bat, bees, etc... will move in and plug things up.