I'll take the easier question first.
For the live attenuated vaccines, they engage and train all parts of the immune system so it acts as one. That includes training the innate immune system, which also has that type of memory that's contained at the epigenetic level, and mobilizing the awareness of the adaptive immune system to respond appropriately to a given type of pathogen. Multiple studies have shown that this type of training provided by live attenuated vaccines protects kids not only against specific pathogens that are a target of the vaccine, but they also provide a more broad range of protection against immune pathologies.
For example, the BCG vaccine, which is a really old-school live attenuated vaccine, is now being tested for the treatment of type 1 diabetes. Young immune systems require this education and exercise, if you will, to function properly, just like other complex systems such as muscles, bones and language acquisition.
In respect to women, this is not new. It has been forever. I think a large part is that drug development doesn't want to make anything more complicated than necessary, and looking at sex-based differences has been ignored across the board. However, I think when it comes to the immune system, given the profound difference, it is unfortunate that we continue to just have a regression to the mean, essentially. That is what we do, and women tend to bear the brunt for things like vaccination. We really should be looking for more sex-based analysis in terms of dosing and safety.