A bin is a small thing so you don't need to go far to get 'to' it - hence 'in' is more natural. On the other hand, a dump is bigger and probably further away, so 'to the dump' is more likely.

Both are acceptable, but "in the bin" sounds more natural. "Wastage" sounds strange to me. I would just use "waste".

Either one works.

I made up this sentence to put preposition in context. I saw sentence with IN which sounds unnatural to me.

Either could be correct but both seem unusal things to say. Why are you saying this and who are you saying it to?