Does exercise improve male fertility?

Moderate, yes. Moderate exercise is good for anyone trying to conceive. More severe forms of training at a competitive level can become a biological stress that can reduce fertility.
Possibly . Not in a well defined male factor infertility case. I suppose one may consider that a healthy lifestyle overall may prove ones fertility though.
Yes. Absolutely. In moderation. See: http://theturekclinic.Com/not-sitting-sitting-disease-mens-health-heart-disease-obesity/.
Yes. Moderate exercise, either weight lifting or cardiovascular, does improve sperm health. Conversely, obesity negatively affects sperm counts and motility and therefore i encourage all my guys to adopt a good work out regimen--it also boosts libido which can't hurt the fertility process!