Citizens of the Republic of Panama, are they allowed to enter China with the new 72 hour free visa?

Citzens from this country are unable to enjoy the 72-hour free transit, since the country's name is not listed in the 51 countries. If the transfering time is less than 72 hours, they are able to enjoy the 24-hour free transit to visit China.

So, if e.g. a Panamanian citizen, has another connecting flight from the same airport within 24hours but has to get the luggage to check-in again for the next flight, how can he/she make usage of this 24h rule? Will there be a special check-in counter in the transit are where the luggage will be received and checked-in again or is there someone who take me from the migraton desk to the luggage claim area and then to the check-in again and then to the immigration again?

Yes, you can make use of the 24-hour free transit policy. There is no speciak check-in counter, you can ask the airport staff to show you the way.