1 - yes that is a great sign. Usually beer starts fermenting in 24 - 72 hours. You must have done a good job aerating your wort.
2 - your friend is in correct here. Do not bottle after one week, it is not near long enough for fermentation to be complete. More like 14 - 21 days and in some cases even more. The best way to judge fermentation is to take gravity readings. The easiest way to do this is to get a beer thief (turkey baster), sanitize it, open up one side of the fermenter, steal the beer, then take your reading.
3 - yes 3 weeks is how long I wait until I even sample the beer. If it tastes good, then I begin to chill it. Some people chill for 3 weeks before they drink.
I hope this helps.
Bottled - Yellow House IPA
Bottled - Citra IPA
Bottled - Redlight Ale (American Amber Ale)
Bottled - Pineapple Ale