It really depends on what kind of exercise you do, and the level of impact it has. I wouldn’t recommend you doing it daily if you’re under a low-calorie diet. But if you’re eating normally, and having enough rest so that your body can rest throughout the day for the next day. If you are I would recommend it, it is a lot more helpful i you do it daily!
There are a bunch of exercises you can do at home with no help from weights or equipment whatsoever. Like Lauren said you usually use your own body on these. Some examples could be push-ups, burpees, jumping rope, squats and sit ups. There are many videos and workouts on social media which you can use, or you can even get creative and make them yourself with exercises you like and feel are effective.
I agree completely with what Trinity said. Stretching is actually a very important part after the work out and I’d even consider it necessary so that all our muscles can actually find a way to be released. I’ve found from experience that when we don’t stretch we do suffer from pain and soreness afterwards, more than normally!