Just discovered this thread... After an overweight landing you definately have to check the Brake Temperatures. Your approach speed will be very high. The tyres can take the punsh, don't worry, but the brake have to absorb the whole deccelaration.
As for the approach speed in heavy rain... In no Boeing Manual whatsoever there is a statement that you have to increase your speed in heavy rain. Normally heavy rains comes with turbulance, and for the turbulance or wind you increase the speed. But also heavy rain comes with a wet (or even worse), flooded runway. You certainly don't want to land with excessive speed in these kind conditions.
But then again, we are talking about JAA, and they want accademic textbook answers. Probably by some CAA pencil warrior who never so an aircraft from inside.
Good luck with your exams.
You will do fine!