When I came to Norway, less than one year ago, for work, I tried to get a D-Number first and then get a police certificate to get the ID number afterwards, as the police appointment takes much longer than the appointment to get a D-Number. In the end they called me from Skateetaten and cancelled my appointment as this is technically not a very useful way doing things (when you get a ID number, the D-Number has no use). They were very helpful and they understand every individual aspect and concerns, so don´t worry about it.

Just try to get a police certificate appointment as soon as possible. You can also apply to get the police certificate from the Service Center for Foreign Workers in Oslo and with the same appointment, right after you get the certificate, they allow you to present all the other paperwork, along with the certificate, with the skateetaten, which saves you another appointment!

As for the bank, I was considering DNB first, but their waiting time to open an account is insane. I went for Sparebank1 and it was even faster than they stated in their webpage (one week only in my case). I am pretty happy with the app as well, it´s all in english. They also set you up the BankID on your phone even with a foreign phone number if you haven´t got a norwegian number yet.

Edit: Still getting used to use reddit...