These are true, not rumours, but not new either.
Chinese government do not allow dual citizenship. If you obtain other countries citizenship, you automatically lost your Chinese citizenship.
The upcoming census will remove the Hukou of those living overseas long time and have resistance. Not the ID. Hukou is what the Chinese government allow local resources. E.g.education, medical care, eligibility of buying properties etc. If you don't live there, doesn't have material impact anyway.