Can I put things like collectibles and maps that I got with the Explorer's Pack in a bank somewhere so another of my characters can use them? I no longer want to play using my first character I created but he has the items I want to transfer.
Your bank is shared by all characters. You can trade stuff between them there. This includes all bound items, as they are bound to account, not the character. If you have maps from the Explorer Pack, you'll need to take them out of the box first, though it will save you space if you leave them in and take them out as you need them one by one. Also note you have direct access to items in your bank while at a crafting station.
Your bank has 60 slots to start with. You can pay gold to increase the number by ten, but the cost goes up each time. There are no other fees to use the bank.
A stack takes one slot. Most items that can stack will stack to 100 or 200. Items with individual stats, like weapons, do not stack. That is set, and does not change in or out the bank.