[question about Transmit/Receive PL Tones/CTSS/CG, etc]

It sounds like they have a tone set on both transmit and receive.

 

For you to join their conversations all radios must be programmed with the same tomes.

 

I think your radio doesn't have any tones enabled, so you can hear everything. Neighbors probably have both transmit and receive programmed.

 

Without knowing make/model of all radios involved I can't help with second half of your question.