Is it legal to go to the Internet cafe and take me back to the police station to manage the cage without my ID card?

Of course it's legal. This is legally called summoning, and the summoning time is 12 hour. Although it is a violation of the Law on Public Security Administration Punishment to go to an Internet cafe without an ID card, because the crime is very light, it is generally not handled, only education or fines are handled, and people must be released after 12 hours. You can recall whether you were detained for more than 12 hours. If they exceed the detention time, they can be prosecuted in the procuratorate.