Software that determines whether a molecule can exist and draw it from a formula?
I believe this website will be of use to you

http://molview.org/

It appears to take names, formulas, smiles etc. If the name/formula/smile ID pops up in the search bar, it will draw it for you. Its database seems quite large, I use it for some pretty big drug molecules.

It draws 2D and 3D images, and it also does single/double/triple bonds.