Passport valid beyond (over 8 months) length of stay. Traveling from USA to LHR and staying 2 nights in London before onward direct flight to JNB for holiday of 20 days.....then direct flight from JNB to LHR connecting 5 hrs later to USA flight.....not leaving LHR.

I counted 9 blank visa pages in my passport......UK requires 1 for my inbound flight.....I don't believe I need another for my return flight since I am connecting.....correct?

South Africa requires 2 blank pages for entry/exit......is this correct? Or do they require 2 blank for entry and another 2 for exit?

Sorry for this OCD question but I'm trying to decide whether I should send my passport for additional Visa pages for this trip.