Eating first thing in the morning is a good habit to have and after a few days you'll find you're waking hungry. Tea and coffee are appetite supressants so try cutting back or switch (at least a couple of cups) to a more natural, lower caffeine tea like Jasmine.
Guilt after a marriage breakup is sooo normal (even if you are the injured party) your children will be happy if you're happy. Remember you did the right thing, a hostile, turbulent atmosphere would have been damaging for your kids and soul destroying for yourself. Try to move on, try counselling if you think it'll help and stay away from anti depressants. You will get over this and find happiness again but happiness doesn't lie with someone else - only you can make you happy, no one else.
Stop worrying about stuff you have no control over. It's wasted energy. Concentrate on stuff you can do and stop beating yourself up. You sound like a nice man and someone who genuinely cares. Clap yourself on the back and count your blessings, I'm sure you have loads when you sit back and think about it. Take care xx