It looks like Mint only does monthly, multi-monthly, and once for its budget time frames. You could just put [365.25/12/7=] 4.35 times your weekly amount into your monthly budget and tell it to roll it over. It will average out. Kludgy, but it's a start.
Mint guesses your bill amounts based on your last bill, and maybe based on information from the bank. You can ignore the $0. It might eventually figure it out, and it might not.
For the second topic, Mint doesn't have anything better than what you do already.
http://satisfaction.mint.com/mint/topics/tracking_physical_gold_and_silverYou could change the value just once a month. In the long run, that's probably the shortest time scale that you will care about in terms of net worth.