Can I cook slow cooking dishes in induction cook top ?

An induction cook top refers to the interplay between certain metals and an electric heat source.So, sure you can use it to slow cook whatever kind of dish you want (on the top of the stove). Just set to a low heat setting for a 'slow' cook'.The oven portion of the stove is NOT heated by induction.

Low & slow dishes can work in the oven or on the 'stove' top, its just more convenient to do it in the oven, because its out of the way.

Yes. I have used Le Cruset (enameled cast iron) dutch ovens on an induction cook top for years. At lower temps the cast iron heats evenly and does a good job of braising. My cook top has temperature selection and I keep it low and slow, somewhere in the 220° range.

Yes, you can do that

Sure you can but if it is going to be cooking for a long time the oven would be a better option. Much more even heat that surrounds the pan not just bottom heat. 

Depends on how long you will be cooking it. If over several hours, i would just buy a crock-pot. They only cost about $40. And you will use it multiple times.