It's actually quite normal and it can be due to a whole host of reasons like restlessness, discomfort, night terrors etc. A regular bedtime routine might help with this e.g. a bath, some milk, gentle rocking and a quiet ambience. This article shares more :) http://www.livestrong.com/article/216652-why-wont-my-3-month-old-baby-sleep-through-the-night/
My baby loves doing it too! She's a little karate kid :) we let her sleep in a sleeping bag so she can kick as much as she wants in the bag ;)
It's normal but there might be a lot reason for it to happen. Well you can swaddle baby to sleep so they feel secure and warm
The average age to stop swaddling baby is around 3 or 4 months of age.
We swaddled our baby to sleep every night till about 4 months.
It's normal