1 - Personal preference. ICs are easier to clean, and have the advantage of cooling the whole volume of wort at once, (Great for whirlpooling your aroma hop addition). Plate chillers are potentially faster and use less water. (You can also plate chill and recirculate to do the whirlpooling aroma hop thing too). Plate chillers are prone to clogging, ICs aren't. Without a pump, Plate chillers can be a beyotch to gravity feed if your setup isn't just right.
2 - Just makes things easier. Easier to transfer, almost a requirement if you have a plate chiller, (but again, you can gravity feed, just not as versatile), allows recirculation after the boil for whirlpooling, opens up all kinds of new mashing tricks.
3- heck if I know - I use my cheapo craigslist no-name burners