Is atopic ezema and asthma in infant cause by diet eg. Seafood, peanut, cold drinks etc during pregnancy?

Maybe. A series of studies showed organic milk had healthier fats than conventional milk (more omega 3s, for instance), that the breast milk of women who drank organic had even healthier fat profile than those who drank conventional, & and that the babies born to women who drank organic during pregnancy & nursing had far less eczema. Genetics sets susceptibility, but there are also environmental triggers.
Not necessarily. Asthma and eczema are allergic diseases that may be hereditary or not. In other words, if you or the other parent of your child have allergies, the child may inherit them. There is no data to show that if you are not allergic, consuming any of the above may increase the chances of the child to be allergic.