This info is basically right except you won't normally need a real residency permit to get a work permit. Your temporary residency with the local cops where you live is all you really need and your landlord should take care of that for you. It's true nearly every foreigner working here needs a work permit though many don't have them. The authorities crack down from time to time and hassle employers for a bit but it usually dies down. There will be new rules on employing foreigners coming out soon. Will supposedly end the current 3% rule but make qualification requirements for foreign workers more stringent. Not having a work permit probably won't cause you any major problems but you should make sure your landlord's registered your temporary residence.

So you dont actually have a physical piece of paper saying permit?

Nah, i don't but my landlord has registered my residence with the local cops and i could get one if i need one. But i don't think you'll need it for your work permit if you apply for one under current rules. You need enough papers for that as it is!

Don't worry. You are a temporary resident by living here. You can't be a permanent resident unless you are VN. You just need to be registered at your address and take your passport wherever you go in VN to register at hotels etc.
Your landlord does the paperwork with local police. And if there was a problem with your work permit/visa the authorities are very good. once when i was getting a new passport my VISA had expired and the local police were aware of this, they did not give me a hard time. With passport delays two months later, they stamped a new visa in my passport. It is just about the local plice knowing you are doing the right thing. if there is a delay at your embassy end, they are polite and understanding.