If I had post-partum depression after giving birth to my son, does this mean that my son will have depression when he grows up?
No. Depression has a genetic component, that's true. But, post-partum depression is a particular, situation-specific, concern. While your son may be predisposed to depression due to your genes, in this case the environment, and personality, are much much more important.
There is risk, yes. Studies of post- partum depression (PPD) effects on infants of PPD mothers found poor social engagement, increased fear responses & significant infant anxiety. Treatment helps, and should continue even if breast feeding. It's safe and helps fend off later problems of cognitive, attachment and socialization issues that have been implicated in these children having higher rates of depression later.
Not necessarily. The important thing is to be able to attach and bond to your new born in as normal a fashion as possible in order to prevent future problems with your child.