Treatment of Every Element as a Set Can we treat every element of every set as a Set or Subset. We know that there are sets of sets like Set of all lines in a Plane. In this set every element (line) is a Set of points. Can we treat points as sets which contains nothing. In other words If N is Set of all Natural Numbers then can it be so that Every Natural number is an Empty Set ?
 A: This is a good question, and I'm glad you asked. It is standard in most set theories to treat all objects as sets, or set-like objects such as classes or semisets. Such as in the cases of ZFC and NBG (two of the most prevalent set theories).
However, as Dave L. Renfro points out, some set theories allow for the existence of urelements, which are members of sets but are not sets themselves.
Onto your question:

If $\mathbb{N}$ is set of all natural numbers, then can it be so that every natural number is an empty set?

The short answer is no. If all natural numbers were the empty set, then by the Axiom of Extensionality (perhaps the most accepted axiom), they would all be equal, which is certainly not a property we would like to have.
However, it is standard to treat the natural numbers as sets. The most common approach is called the Von Neumann ordinals defined as follows:
$$0 := \{\}$$
$$n+1 := n\cup\{n\}.$$
So in this sense, $5=\{0,1,2,3,4\}$. This aproach is nice, because it satisfies that the $n^{th}$ natural number contains $n$ distinct elements. This is not the only approach however. Other examples include the Zermelo ordinals, where
$$0  := \{\}$$
$$n+1  := \{n\}.$$
So, $5=\{4\}$. This approach also has a nice property. Namely, that when treated as a rooted identity tree, the $n^{th}$ natural number has $n$ nodes.
