I agree with Johan that Subway sandwiches may not be a good choice for your total diet. Don't believe what you see on TV. And no matter what you eat, be sure you take a good vitamin supplement. A diet is a stressor on the body and you must have balanced nutrition to be on the safe side.
Diet Coke shouldn't affect your weight loss one way or the other. However, for your information, as you get older you should cut out all sodas. First, aspartame used to sweeten many sodas is poison and has many side effects on people who are vulnerable to them. Second, the sweet taste of the soda sets off certain metabolic responses in the body that makes it come close to processing the intake as sugar. Caffeine isn't particularly nutritious and won't give you the same energy boost as your exercise will. Over a period of time, caffeine will not be a positive thing in your diet.
If I were you, I would quickly switch to good old WATER, you're favorite kind, and hydrate yourself that way. It may not be as refreshing to you as Diet Coke right away but later you will grow to yearn it and you can drink as much as you like (within reason) with ZERO calories and many health benefits. If refer you to this link, put up by Columbia University, that will convince you that WATER is the way to go:
http://www.goaskalice.columbia.edu/0971.html At the bottom of that page is a link about the risks of Apartame, used to sweeten sodas and which also goes under the name Equal:
http://www.goaskalice.columbia.edu/0736.html
As for your heart rate, 130 seems to be at the lower end of the range of what you should be doing but is certainly adequate. To make the computation for yourself, go to:
http://exercise.about.com/cs/fitnesstools/l/bl_THR.htm and insert the data for yourself.
You may not be sweating because of inadequate cardio exercise, which one of the trainers at the gym can help you with.
Before you change your exercise in any substantial way, it would be a very good idea to get yourself checked out by a doctor. Heavy exercise and diet can wreak havoc on your body...even a youthful one...and your doctor can make sure you are prepared. You may even have medical issues about which you are totally unaware and which could be affected by your new exercise regimen. The possibility is slim but death is so permanent and it does happen for some.
Good luck!