Boarding school with emphasis on stem

Oundle don’t currently have a preference test but you need to have registered and chosen a house by end of year 6 early year 7 I would say to be sure of a place. It’s highly popular. It no longer offers any scholarships for example.

Wycliffe has a wide range of international students and offer all stem subjects. It is relatively small compared to the others on the list (DC don't attend, just live close.)

Where are you in Africa?
There are good boarding schools there.
If you are in interested in IB rather than IGSCE there will soon be 2 UWCs - one in Swaziland and one in Tanzania.

I am not sure I understand what you mean when you say that none of these schools offer STEM at GCSE. All private boarding schools in UK offer maths, chemistry, physics and biology at GCSE. They would not survive if they did not.

Some offer the IGCSE qualification. This is a result of the GCSE having changed so much in recent years. They may move back to GCSE in the future because it has become more rigorous as a result of changes brought in in 2016. But most are waiting to see how it pans out, and for the moment the IGCSE is essentially the same qualification and is treated as such for the purposes of sixth form/university entrance.

All private boarding schools - with the possible exception of Winchester College - place a heavy emphasis on sport. All boys schools are usually stronger at sport because they have larger numbers to pick from.

As an overseas parent you will want a school with FULL boarding where a majority of boarders are in on a Saturday night. Oundle and Rugby are the only ones on your list ( I think!) that tick that box. You could also look at King Edwards Oxford, Marlborough, King‘ Canterbury (all co-ed) ,and Sherborne Boys. Charterhouse and Bradfield definitely empty out on Saturdays and your DC may be left as one of a small group in the house

Most UK boarding schools are fairly international so I do not think racism is a big issue in the boarding houses - though there may be incidents from time to time. They should all have a policy on addressing it.

You need to be careful not to miss the dates for registration and pre tests which sometimes take place in Y6/Y7.

I can add some insight into Oundle. Half of all pupils take Maths as an A level. Its a school with great emphasis on STEM subjects backed up by a phenomenal STEM building which is very inspiring. Sport is also very strong there. They do not bring in big sport scholars at sixth form as some schools do.
There are 7 boys boarding houses each with around 60 boys plus a similar number of full boarding girls. There are then around 200 day pupils located in their own day house. Full boarding at Oundle is fixed. There is NO weekly options. There’s one weekend exeat per term outside of the half term (all schools have half term for a week or two each term). I think it’s one of a handful of proper full boarding schools left. Many boarding schools have an exeat at least three weekly if not offering weekly options so do your research on other schools.
Racism is not an issue at Oundle in line with many British boarding schools. There are approx 15% overseas students at Oundle. Many from Asia but also from Africa. The African boys , particularly, integrate well into school and sporting life.

It’s an academic school so those below average would possibly struggle.

Not sure what you mean by a full range of STEM subjects. Sciences and Maths are universallly taught. Which sports are you interested in , some schools will prioritise rugby, others football, hockey, cricket or swimming etc. Are you looking for an urban or rural setting, access to which airport, family or friend links and so on.

What's your budget for fees?

Most big name good boarding schools (some would say not all those you’ve listed are big names) offer a full range of stem subjects physics maths biology maths etc at GCSE and A levels. I personally have never heard of one that doesnt. Malvern I believe is full boarding as is Rugby. Bradfield is basically weekly boarding as is Cheltenham and Wycliffe I’m not sure about Oundle Stowe I think it’s a mix of day and boarding. The others you will have to enquire very carefully remember about ask very specific questions e.g exactly how many children in this house/yr are full boarding schools schools are notoriously very economical with the truth.
Oundle I believe has a good reputation for science and I seem to remember years ago being told very few exeats. I suspect you’ve missed the cut off date for Charterhouse as they ore test in yr 6, you could also look at Kings Canterbury which is also mainly full boarding and Marlborough which is also full boarding but again you might be too late as it pre tests in yr 6.,
Most boarding schools have 10-20% international pupils I don’t think racism is a problem.