Firstly, I am not a professional medical/bio-chemistry scientist by any stretch of the imagination - so I don't have a massive reference of studies to reply with and am not going to give as effective a reply as a seasoned specialist would do. I have put a lot of time though, into listening to many doctors who are qualified and well researched enough to respond to these issues in full depth - so while I don't have an answer to every question, I do have an overview understanding of the issues involved and could probably get the answers if needed by emailing relevant people.
It would be nice to think that these issues are clear cut and fully agreed upon, but it appears they are not. If we look at many websites they state clearly that a child's immune system is not capable of defending the child until the child is a few months old and that they are dependent on their mother for protection. However, published science documents make clear there is controversy and investigation ongoing about that.
This page from 2014 describes how there is speculation that baby immune systems might be more capable than previously thought and I have read other pages that go into a lot of detail rejecting these claims that baby systems.
In 2003, Pihlgren showed that if mammals are vaccinated too early, memory IgG responses to T-cell dependant antigens are suppressed. In mice it took 6 – 8 weeks for the immune system to mature enough to be able to start making long term Ig G antibodies. Pihlgren stated that in humans, the process is much longer, without specifying how long.