There are 13 member states that are party to the scheme and in each member state there is a bureau ( National Bureaux) which coordinate the overall operations in the country.  It is this National Bureau, in consultation with its members, that fixes the rates to be charged for yellow card issued in its country.

The Yellow Card issued by a country, is an extension of the insurance cover in its own country and has nothing to do with the insurance cover in the country being visited.

The rates take into account risk factors. administration cost , which include  the type of vehicle , CC, number of  countries  visited , length of visit , extent of liability in each country, etc . The rates also take into account administrative costs, claims and underwriting experience. Therefore, what Insurance companies in Zimbabwe charge for trucks travelling to Zambia and DR Congo is different to what  Insurance companies in Malawi charge for the same risk.  Each county has its own rates.

Taking into account the above, I will answer your questions as follows:

Does Zambia set the Yellow card rate for foreign trucks entering its country?

No, it is set by the Yellow card issuing country

Or, if it is a Zimbabwe truck entering Zambia, does Zimbabwe set the rate?

Yes, it is set by Zimbabwe, because the card has to be issued in Zimbabwe

Furthermore, will a DRC truck, which obtains its Yellow Card in the DRC, pay the same charge into Zambia, as a Zimbabwe truck which obtains its Yellow Card in Zimbabwe?

No , the rate set by Zimbabwe and DR Congo for truck entering Zambia are not the same. Because Zimbabwe and DR Congo have difference way of assessing the risk in Zambia and their administrative cost and others factors are not the same .

Who decides whether there is a charge for the truck tractor separately from the trailer?

In insurance they are called UNDERWRITERS, they are the one who fix the rate for truck tractor separately from the trailer. Normally rates are fixed by considering the following elements: risk factors ( they are defined and are many) administrative cost, margin of profit and claims experience. Based on this they fix and publish their rate , which would be reviewed from time to time. They have different rates for private cars, buses, trucks, trailers and those used for private , commercial , hire etc