Can I lose fat by running and brisk walking?
Absolutely if you do it regularly and continuously increase either your speed or distance - or both. You need to start by doing less than you think you can and steadily increasing the amount you challenge yourself. Learn to enjoy your body in movement and to tolerate being a bit short of breath.
It helps if you also reduce the amount you eat and drink. Water and unsweetened herbal teas/infusions are free, but consuming sweetened drinks, sodas, juices and excessive dairy can stop weight loss despite increased exercise.
After I'd been walking for a month or two, I took a bus going the wrong way. I got off when I realized my mistake, but it was late and busses were no longer going in the other direction, so I walked four miles to a place I could catch a bus home. I hustled because I didn't want to miss the last bus which would pass in less than an hour. I made it to the bus stop in well under an hour. I was proud of myself. My body was able to do what I needed in a situation I needed it. And my body got thinner as I got more fit.
Keep walking and running, keep challenging yourself and keep at it. Just keep going.