The questions you are asking are the kinds of questions that come up when people hear "sound bite" fitness comments. The problem with sound bite fitness statements - things like "you have to work out for 30 mins for it to be useful" and "working out on an empty stomach burns more fat" is that they try to reduce the enormous complexity of how your body works to a few words - which simply can't be done.
Do you need to workout for a solid 20-30 minute block? Yes. And no. As far as weight loss goes, the idea is total calories burned. If you burn 300 calories a day in exercise, doing it in 4 10 minute blocks, then great. If you burn 300 calories a day doing it in one 30 minute block, well that works too. 300 calories is 300 calories. However, you will probably burn more calories by doing a longer, more sustained effort, simply because it's easier to get your heart rate higher and keep it there for longer when you do your exercise in a block. When you're only doing 10 mins at a time, you barely have time to get your heart rate up there before you're stopping.
Which leads to: From a cardio vascular standpoint, there is more benefit to doing a solid block of exercise of at least 20-30 mins. Raising your heart rate and your breathing rate for that long builds cardiovascular endurance, which is one of the other non-weight loss related benefits to exercise.
But the bottom line is that getting up and moving makes a difference. So if you walk for 10 minutes a few times a day, and if that's more than you used to do in the past, then it's beneficial.
As far as fasted cardio - I have yet to see a study that shows enough benefits from fasted cardio to make a difference. And, for some people, working out on an empty stomach makes them sick or weak or less efficient. Ultimately the best method to use is one that works for you. If you feel that you're working more effectively on an empty stomach - go for it. The psychological benefits are as important as anything else. If you, like me, get queasy when working out hard on an empty stomach, then it's a good idea to have something to eat 30 mins to an hour before hand. Either way, you're not going to increase your fat loss by any *significant* amount ... so it just plain doesn't matter.
