Is it safe for an obese person to exercise in order to lose weight?

Yes. It usually is safe for obese patients without diabetes or heart disease to perform mild exercise such as walking, but prior to starting more strenuous workouts patients should see their primary care physician for a check-up.
Yes. Need to build endurance - so take it slow. Make sure it is not sarcopenic obesity - low lean muscle mass - there is a danger of gut/cardiac infarction - get a body composition analysis and a structured workout program.