As far as commas are concerned, the first two sound correct to me, while the last one does not. Someone with more knowledge of formal grammar rules might be able to give a more exact answer, but to me
The artist painted this portrait using watercolors
I would guess this has less to do with the difference between restrictive and non-restrictive clauses, like in the link you posted, and more to do with the word "using". In your example, I believe "using" is acting as a preposition and not a participle. For example, the sentence is equally valid as:
The artist painted this portrait with watercolors.
The policeman stopped the criminal using a stun gun.
could be understood as
The policeman stopped the criminal with a stun gun.
Importantly, there is ambiguity in the first one about whether "using" is a participle, which would mean the criminal is using a stun gun, or a preposition, so in this case using "with" would be preferable. Because a portrait can clearly not "use" watercolors, 'using' only makes sense as a preposition.
Good question, though.