As a father myself I believe that a good father should have all the traits you mentioned above. I agree that there is a balance between authority and support. I tend to think that I am doing a good job of it, as my kid is "scared" of me in that he does worry about whether I would get angry (the authority part), yet I am still his favourite play buddy which makes my wife jealous. This also comes down to a lot of play, just put yourself down and play with them at an equal footing, doing simple silly stuff like pronouncing words wrong or just chase them around or play hide and seek with them, all these would increase the bond between you and your child.

The one thing that I think I need to work on, and something that a father would need, is patience. Sometimes when we want them to succeed, or to become independent, or doing homework etc, we tend to forget that they are just kids, and just need more time to understanding something or to learn something, or even just more time to get from a state of excitement to calmness. We must try to be patience and let them have the time they need.

My family was in a similar situation, with my mum passed away when I was very young. I know my Dad suffered a lot, so I understand what you feel and what a great man your Dad must be. He must be very happy to have a grandchild coming his way!