/diy/ - Do It Yourself

Could anyone explain this circuit to me? It's supposed to be XNOR gate.
I understand how it forks for the most part, but I don't get 2 things;
When A and B are live, and the current is shorted away from Q3 base, why it isn't shorted on the diode?
Also, what's the exact purpose of resistors here? I built this circuit and noticed that it doesn't work properly when resistors are removed, so apart from protecting the components they seem to balance the whole circuit somehow but I wasn't educated in electronics and I don't understand this phenomenon.

Also, do you recommend any sources to learn electronics?