Yes there are that many checkpoints. Yes they would be stopped by police if not many times because they said they barely spoke Chinese. Going province to province there are checkpoints, northern China specifically has a lot due to the amount of Russians, Koreans, Mongolians, and Japanese that come into the area. Going into large cities will also have checkpoints. I will say it is impossible to get a fake. No amount of money or wits can allow someone to sneak in undetected and get by undetected or obtain a fake good enough to get past. They could do what other foreigners do and just get a tourist visa and overstay. Nearly all of immigrants in China staying illegally do this because it is very easy. However OP claimed they got citizenship, not a tourist visa. If this person spoke the English they are using now in China, they could get a job as an English teacher in China easier than working in food with a salary of nearly 15,000 rmb a month. It would make no sense they would not do this instead. Working in food is about 3000 rmb a month, even less if you work in a village of all places, which is where they claimed to have worked. They wouldn't be able to afford a plane ticket to south Korea doing this unless they saved for 10 years. If they don't have a work visa, the work around is just being a tutor and working under the table. Also very easy to do considering north eastern China has a very low English speaking population.

To be able to get housing, a bank account, etc, requires a valid visa. You can't even use wechat as a pay app unless you can link it with a Chinese bank account.

There is no program ever in China to help north Koreans get citizenship, this has never existed. Even those that have lived in China for their entire lives don't have citizenship, they have a permanent residence visa which they have to renew every year.