I think Diadem is fine at $6?
Bank is $7, but it's quite easy to make Bank worth more than Gold.
With Diadem, it's a bit harder, and if it's $6, well, it's just the same as Gold in BM.
Bag of Gold I would price at $8. Non-terminal Gold topdecking is pretty sweet. $7 seems just a tad too close to regular Gold.
Trusty Steed is like a powered up City with a lot of versatility, so I'm thinking $7.
Princess' only drawback is that it can't be throne roomed, but it's still pretty powerful. Bridge is $4, so this big brother I might price at $7 or $8.
I would suggest you just playtest and see for yourself.