Welcome to the forum! I have an adult RES that I had to train to eat veggies/fruits. This is how I did it (read all the way thru the thread because there are updates as well!):
http://www.redearslider.com/forum/viewtopic.php?t=3998
30gallon tank is way too small for your 5"+ size RES. Turtles love to swim, so start making a plan to upgrade the tank to a larger one. I have my 9" RES in a 90 gallon tank and she loves it because she can spread all the way out & not touch the bottom. Fill up as much as you can! Your baby will love you for it.
Also, I don't know if you know, but nowadays cleaning a super large tank is not a bucket-by-bucket job. They have something called a "python" tube which hooks up to a faucet in your house & sucks the water out of the tank when you run the faucet. Then when you flip the valve on the python the opposite way, the python will FILL your tank. NO HAULING buckets!!! It is the greatest thing ever. So don't be scared of a bigger tank because of cleaning. It's not bad, trust me. I was worried when I went to my 90-gallon but it is working out great.
My turtle is almost totally black in color on her belly so that is normal for some turts. Also, the bottom of the shell (plastron) tends to peel as you described, more in "mica-like" sheets that are thicker. Also normal.