Colour has nothing to do with health or temperament , not in Cockers anyway (I know there are some issues with colour and health, white boxers, merle to merle in collies etc so colour does have relevence elsewhere with regard to health but I don't know of any link to temperamant) Its good you are asking questions and here is the place to ask anything about Cockers, so in answer to your question
a, No Blacks don't have a better..... or a worse temperament than other colours
b, no they are not more prone to illness (my black girl is 3 and has no health issues whatsoever touching wood so as not to jinx myself
)
I have Golden/Red and a Black and would recommend either any day of the week
Most important issue is to go to a reputable breeder, ensure Health testing in place and that you see pups with their Mum then you have to keep up socialisation and positive training methods, good diet, to ensure you have a happy , healthy Cocker
Good luck in your search