Is it permissible to eat food provided by governmental institutions in China that grant certificates for "halal" or similar designations, given that investigating the standards of these bodies or the producing companies is difficult?

It is evident that the questioner suffers from severe obsessive-compulsive disorder (waswasah). The products he inquires about are mostly pure, even if their original ingredients contained impurities, because they undergo a process of transformation (istihalah) during manufacturing. Istihalah is a purifying agent according to the preferred opinion, and this is further confirmed by the certification of the competent authority regarding their permissibility. As for the food that requires investigation, it is slaughtered meat in the questioner's country, for the default status of slaughtered meat there is that it is not Islamically slaughtered (dhabihah (definition) shar'iyyah), and one acts upon the default status when in doubt.