Embeddings and connected sum

Question

Let $X$ be a compact connected oriented smooth $m$-manifold. For any compact connected oriented smooth $m$-manifold $W$, consider their well-defined connected sum $$X \# W.$$

I wanted to ask two basic questions about this operation:

1. Is there always a smooth embedding from $X$ to $X \# W$?

2. Can we realize $X$ as a submanifold of $X \# W$?

EDIT: Assume that $X$ or $W$ not diffeomorphic to $S^m$ since it gives the identity element for connected sum operation.