The quote for USD = 1 USD The quote for EUR = 1 EUR The quote for JPY = 1 JPY Quoting singles doesn't make any sense.... since nobody is selling USD for USD. Only USD for EUR or EUR for JPY... hence the pair... Quote for EUR.USD = 1.235 Quote for USD.JPY = 108.70 etcetc
Because you have to use another currency to buy a currency, e.g. you can't use USD to buy USD, as each is worth the same, 1 for 1, so there'd be no point. Buy buying a currency makes sense on expectations: so what you buy today can be sold next week for more than you paid.
Because you need to measure the currency against something. You could measure all against gold for example, to get the same feeling just how much gold you can buy in any particular currency.
If you are travelling abroad you might first go to the bank and exchange one currency for another. Or once you arrive at your foreign destination. In others words how many X do you get for your Y. That is expressed as an exchange (aka trade) rate. Same thing occurs when you purchase something. Dollars or whatever are exchanged for goods or services. Basics.