It's exactly how it works. It's multiple entry, so you can re-enter on the day it expires and get stamped in for another year. I should know. I've done it twice myself!
I think it's related. Using an agent more often than not involves a bribe being paid, which is illegal. Many people downplay this by calling it "tea money", but no matter how you spin it, it's a bribe.
Absolutely it depends on the immigration office, but for many people, they have to leave Thailand, re-enter on a tourism entry, and restart the whole process. Thankfully, I'm in a financial situation where I don't need to pay bribes to get an extension!
If an agent is bypassing the 400k requirement, it means they are paying a bribe to an immigration officer. It's not a good situation to get into, as it means you are tied to that agent forever. Best to do it legally yourself to avoid problems down the track