2yr olds are in their exploring stage. So long that it is safe, just let them explore by themselves. I never have to follow my son to every where he go. I just use my eyes to follow him. of course he is always about an arm length or two away from me.
Regarding your point 1 & 2, exercise firm n consistent discipline. Punishment (time out, naughty corner etc) if he still does not listen after 2-3 (max) warnings. They are trying to see how far their "mischief" can go.