It's a very complex subject!
Try reading
www.diabetesnet.com an American site (so the numbers are in the US system unfortunately), but it has a very good section on exercise. It explains about carb replacement, insulin reduction and a combination of the two.
There's also the UK site
www.runsweet.co.uk which is helpful if you can spend the time trawling through every page until you find the link on the page to the other page to the other link to the info that you want (I tend to lose the will to,live trying to navigate this site, but if you have patience, the info is ther, just in a rather random order).
The general rule is that Glycogen replacement starts a couple of hours after exercise and continues for 24-48 hours. If you exercise more often than every other day, your insulin needs will be constantly reduced to compensate for your liver replenishing its glycogen stores. If you exercise less than every other day as I do), you need to reduce your insulin intake for up to 48 hours (I find about 18-24 hours works for me after a 45 minute swim, but it was trial and error getting there). I am on a pump, so I reduce my basal insulin by about 15% from 3 hours after the swim until the next afternoon. I'm not completely sure what you do on MDI, I think reduce your long-acting insulin nightime dose, but it's worth speaking to your HCP to confirm.
However, if you exercise at least 4 times per week, you shouldn't need to do this at all. If you stop exercising (due to injury?) you'll probably find that your insulin needs rise by up to 20% as your body doesn't need to replenish all that used up glycogen all of a sudden.
I can't help at all with the body fat/diet thing I'm afraid, but perhaps I've given you something to think about.