1. Yes it's perfectly normal for them to kick around. He is discovering his mobility and he is able to gain control of him limbs.
2. 6mo are still young, i would say by then you shld be able to set a rountine of nap time and meal time.
You can play peekaboo or those soft block for him to 'stack' Yes i usually bring for a morning walk.
3. It sounds like teeth. You can try increasing the milk portion to see IF he sleeps longer
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