Major rule for care settings is the working partnership between the setting and parents, a positive relationship will come across to the child helping them feel at ease... also the parent will be more incline to listen to you. It is important you build a positive relationship with parents as that enables u both to work closely together in which will benefit the child in a variety of ways. this will be in: settling a child, sharin developmental info, and also learning about childs interest + family routines. parents have an strong bond with their child and will want them to be protected so it is important they feel u r safe and trustable with their child. a positive relationship helps to allow the parents to become involved as they will have vital info on their child and you may be able to observe a change in the child when parents are there.
I am unsure completely why it says including fathers but if it was me i would put in a few sentences saying that sometimes the mothers of children can be protective and seem the ones to be very forward in creating a relationship however fathers too should be involved as a male role model and also as he too will have a protective instinct that he must feel also that the child is safe and you are trustworthy. Also it could be seen as discrimination of gender if you favour the mother with regards to information sharing and building a relationship.
the second question reserach about the EYFS framework - if you live in England, Foundation Phase for Wales, and how it includes parents look at the policies you follow for example you should have a working in partnership with parents and carers policy in which will state reasons as to why it is important (also will contain answers to your first question) overall it is to ensure the parents can get involved happily and know exactly what to expect as well as staff members...
Hope this helps a little :S xx