Just some Qs for any locals to help me get my head around driving a motorbike here...
These are mostly good questions. As dangerous as driving is here, it is even more dangerous to ignore the local customs.
I've noticed many people on bikes here don't wear helmets, and do run red lights. What are the rules on this, and why are so many allowed to ignore them?
Vietnam actually has very high compliance with the helmet law, and lack thereof is one of the few things regularly ticketed by traffic cops. Yes Vietnam has laws against running red lights, speeding, driving the wrong way, on sidewalks, etc. Why are the laws not enforced? We don't know. I never see police cruising for rule breakers, they only setup checkpoints. I think the police-to-population ratio is very small.
As a driver approaching a green light, when might I expect that someone sitting at a red light crossing my street will run the red light? I've found the key to driving safety is being able to anticipate the actions of other drivers (signal when turning, etc.), ...
In the US, "running a red light" almost always means a person didn't see the signal and just shoots through, like it is green; it is an accident, not a deliberate decision. It is rare there, and it is rare here.
The common activity here is that a driver will approach the intersection and self-justify: "no cops in sight, I am in a big hurry, I can make it if I just dodge these other vehicles". It is an anarchy that you never see in the US except at 3:00am.
... but I can't figure out when I should anticipate this.
Driving Rule #1 in Vietnam is don't hit anything. Rule #2 is drive defensively. I have never seen better defensive motorbike drivers. It takes trust in peripheral vision and split-secod timing judgements from experience.
(Just motorbikes though, you put a Vietnamese in a car, and they short circuit.)
Are people who follow traffic laws considered to be losers, foolish, etc.?

Why don't Vietnamese criticize each others driving? It could be that I just haven't seen it or don't understand it, but based on my experience in America, if you drive poorly, other drivers will be happy to let you know.
You will learn that Vietnamese are normal people like everywhere. Some are successful, most all are law-abiding and avoid trouble, a few are jerks. Don't judge people by their driving skills, I lived in Germany and Germans were Mr Hyde on the road, Dr Jekyll in person.
You need to live in a different culture for awhile to learn about your own. For example, Americans live under a million laws and are very law abiding, yet quick to moral outrage when a person upsets social convention. Which leads to cries for more laws to be self righteous about. Protests, road rage, whining, law suits: that's America.
My Vietnamese family is not judgmental, nor were Thai or Indonesians when I was there. It is called "live-and-let-live", living under a lot more personal freedom than you are used to.
We just moved into an eagle's nest 24 floors over a busy intersection, in a wilder district of Saigon. From here, I estimate only 5% are red-light violating traffic anarchists, 5% drive on the wrong side, though sure, 25% will jump the sidewalk when there is a breakdown on the bridge.
I've noticed many motorbikes will have a face mask covering the number plate on the back. What is the purpose of this?
I've never seen that. Must be a good place to store masks.
Thanks in advance to anyone who can help me.
Have fun. A motorbike is the best way and the Vietnamese way to get around. 