You may as well be honest about the due date - everyone will want to know and most people don't go on their due date so it doesn't really matter anyway.

Don't tell anyone that you are in labour unless you want them at the hospital and therefore probably in the labour room with you. I wasn't intending to tell anyone until I was well advanced by my DF got overexcited and called both my mum and his mum. This resulted in having his mum at hospital for much of the labour as well as my parents there for some of it. I had only ever intended on my DF being in the labour room with me but I think it worked out well to have the family support as well. My labour was a long (17 hours and 12 hours or so of pre labour) so he did need a bit of a break at times. Having the others there allowed him to take a short break leaving me with someone there to hold my hand or rub my back.

If you are intending to share news with your BB due date group be careful about sharing your phone number. I've noticed some people get inundated with messages from people when they go into labour. That can't be fun for your partner to deal with - as they tend to end up with your phone while it's all going on.

My phone got left at home so I didn't advise any friends of the birth til the following day. Joint friends found out the day of the birth as their numbers were of course in DF's phone. I vaguely remember having a couple of very weird phone conversations with family/close friends shortly after the birth (DF was way over excited by that time). I was so out of it and I have no idea what I said to them. Might be wise to word DF up to not pass the phone to you after the birth.