1. This is correct. Hu A or Hu C
2. This is also correct. Hu C can be legally purchased if you live outside of the A20
3. This is correct too, the temp residency permit must shown your Chinese name.
4. This to is correct, they will usually just write your Chinese name on the temp permit and then stamp it

If you had all of the above then what was the problem? I remember being in and out of there within 5 minutes.