There are several contenders for the title of the world’s oldest capital city, and all of them are in the middle East and Mediterranean area. This is about cities that were continuously inhabited for thousands of years.
Africa as a continent includes mainland and a couple of island states, so when you speak about capital cities, this can be about any of the two options.
When this is about the westernmost capital city in Europe, one can speak about the mainland or in general, this is about different cities.
There are many old and continuously inhabited cities in Africa, in particular in what is now Egypt where Faiyum and Luxor exist for more than 4000 years. But with capitals this is different.
There are no capital cities of countries exactly on the equator, but some of them are very close to it. Here you have the list of the closest ones.
When this is about the capital cities that are farthest from the equator, one could think about the north side and the south side of the globe. But it turns out that this is only about the capitals in the north.
The term the coldest may imply the average temperature throughout the year or the lowest temperature in a particular winter month. In any case, the answer is below.
If you are thinking of moving to the south and reducing your heating and living expenses, you will want to check this list of the warmest capitals in Europe.
There are two southern island nations with their capitals that politically belong to Europe, but one could place them geographically in Africa and Middle East (Asia).
When this is about the oldest cities in Europe, out of top 8, only one of them is not in the present day Greece, but all 8 of them are the cities of the old Greece.