How can I visualize (i.e. "draw") these shapes $\#^k(S^2 \times S^2)$ the $k$-fold connected sum of the product of two spheres.
This was called the connected sum of two projective planes. Here it looks like $\mathbb{R}P^2$ rather than $\mathbb{C}P^2$. Here $K$ is the Klein bottle.
