[color:"orange"]a) The vendors do not have enough gold to buy all the items you pick up in the game.[/color]
I think that is by design. Jump to the battlefield and trade for some charms or expensive jewelry; they are lightweight and you can get most of the value back trading them (much more than you would leaving stuff behind, anyway).
[color:"orange"]b) When you buy something or pay for training the money is not reflected in the vendor's inventory.[/color]
I was disappointed by this at first, also. However, in practice I have lots of gold (have only used it for teachers), trading loot for potions and equipment.
[color:"orange"]d) Items that I have equipped should not appear in my trade window.[/color]
The price on equipped items is displayed in a different colour, and I have not sold anything I had equipped by accident.
Actually, I would like both character's equipped items shown, rather than just the one doing the trading. If someone is selling a good ring, for example, I have to exit the trade window and either open my inventory or switch active characters and trade again if I want to check the stats against what I already have for both characters.