1) Imagine your have a USD denominated account (HOME currency USD) and you want to buy NZD/JPY. Without a broker you would use the HOME currency account as collateral to borrow money in the QUOTE currency (JPY), convert that money to NZD (known as the BASE currency) and put the amount in NZDs in a deposit (interest earning) account.
In this scenario you are Long NZD (because that is what you have), and you are short JPY (because you have to repay the loan at some time). During the time the position is open you may earn interest on the NZD, but pay interest on your JPY loan. Complicated, but in theory a broker will do all of this for you at the click of a button; I say in theory because in practice, unless you are a large trader, they will just take the other side of the trade as if they were a bookmaker.
If the value of NZD against JPY rises then your overall position will be profitable, if it falls then your position will be in loss.
All of which means the simple answer to your question is that, in theory, you are buying / selling currency.
2) The way brokers make their money is on the spread. The difference between the buying and selling price. The quote for NZD/JPY might be 73.80/73.82 which means that to open a position you pay 72.82, but if you were to immediately close you would only receive 73.80 - a 0.02 loss. Which is why when you open a position like this at the point it is opened it shows a negative value of -0.02.
3) I don't think any broker is going to offer a triangular trade like that, they only trade in pairs. I've heard of trading strategies that involve taking positions in 3 (or more) currencies simultaneously, but I would suggest they are very high risk and expensive as you will pay multiple spreads.