1. To get the Chaos Emeralds, you must collect the 7 SP Rings in one act. When you get all 7 and clear the stage with them(with out dying) you will be sent to a special stage. This is a 3D type Special Stage and you must run around the field collecting rings. You have to get 300 Rings to clear the SP stage and you have 120 secs to do so. To get the 300 Rings, try to make ring combos by collecting rings in succession. Try your best to find 7-9x multipiers. Getting the Chaos Emeralds is a real bitch, good luck. Also, each Zone has a specific Chaos Emerald to get, once you get it there, you have to go in to the next Zone unlike the originals where you can get 2 Chaos Emeralds in one Zone.
2. Yes, getting 28 Emeralds(7 for Sonic, Tails, Knux and Cream) and clearing True Area 53 will unlock Amy. The prizes for the Emerald collection are: Tiny Chao Garden, then Sound Test, then Boss Attack Mode, then Amy. To get the prizes you must collect all the emeralds for 1 character and beat XX Zone with that character. If you get all 7 emeralds with Sonic and beat XX Zone, you get the prize and you get a new Zone, True Area 53.
Edit: By originals, i meant Sonic 2 :P