Hello.

I have a question.

There are diseases like chicken pox, which you only catch once and never again, assuming that the disease doesn't mutate so the immune system can recognize and combat it upon contact without letting it multiply, infect and spread.
Assuming that both the mother and the father had encountered chicken pox.
Why is their offspring not already prepared and resistant to that disease the same way the childs parents are?

Is there no direct sharing of blood between the mother and embryo, does breastfeeding not help either?

This article may be of interest

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4165321/

I suspect others (David?) are better qualified to answer this but broadly speaking, yes there is transfer of maternal antibodies from mother to offspring (via egg yolk in birds, via placenta and milk in mammals like us).  These provide considerable proptection against diseases in very early life but do decay with time - so the protection is not complete and unlimited! Fortunately the offspring immune system, which is often not very competent at birth.hatching becomes fully developed and active. However, it does not "inherit a memory" of pathogens the mother may have been exposed to.

correct.

immunity to infections is mediated by the immune system (antibodies and T-cells) which is an acquired process that ONLY occurs after having had the infection or an immunisation which mimics having the infection.

As Alistair correctly says if a woman gets the infection whilst pregnant and thus has high levels of the relevant antibody then that can be passed to the baby and protection will last for a few months. After that is tends to wear off and the child still needs immunisation to mount a full long-lasting immune response