At this stage your baby has almost finished growing & is more about putting on weight to keep him warm
It is very normal for babies to engage (head right down) weeks before labour. Especially a first baby. Just because the head has started decending doesn't mean its all the way down yet either. It may only be half way & needs to drop a little more
My first was fully engaged at 36 weeks, but wasn't born til just over 41 weeks Don't worry about head size either All sounds normal. Babies head may only be 2cm bigger than average is all