Household plumbing/sewer issues

A description of the plumbing in our single story house in Albuquerque:

Front to back of house:

Bathroom 1 - toilet, bathtub/shower, sink
Laundry room - washing machine
Garage - water heater
Kitchen - sink, dishwasher, ice maker
Roof - swamp cooler
Bathroom 2 - sink, toilet, stand alone tub, stand alone shower
Two outside garden faucets

Symptoms:

Yesterday, while the dishwasher was running, the toilet in bathroom 1 started gurgling air bubbles and losing water level in the bowl.

About an hour later while the washing machine was in the spin cycle and draining water, the kitchen sink started making the same gurgling noises.

A few minutes later, the toilet in bathroom 2 was flushed and it overflowed, then lost all water in the bowl then started filling up with sewage as the washing machine continued the rinse and spin cycle.

Our neighbor/handyman came over and I described the situation. He used a plunger on the toilet in bathroom 2 and that cleared that up, but then sewage started coming up through the drain in the stand alone shower. He used the plunger on the shower drain and that seemed to clear everything.

He then went outside to the sewer pipes in the front of the house and ran water through them to check for clogs in the drainage from the house to the street. Everything drained as expected and there hasn't been anymore gurgling from the plumbing so far.


Questions:

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?