"If I duplicate the article that I wrote would I then risk getting a penalty for duplicate content?"
Not likely a penalty, but no benefits either (unless people start linking to the version on your site of course)
"If so, then what is the best way for me to include the article on my site for the benefit of my readers, but not lead to the duplicate content problem?
Would it be better to use a canonical tag? Or to noindex the page?"
Both would work I think, though canonical would be the neater option (assuming it isn't harming you to help the other website).
"If I use the canonical tag, am I helping to make the article on the external blog stronger? Where is I use the noindex tag I am not helping my site nor that article I think, is that right?"
Right and right
"What about the comments that people write on the article on my site?"
I think (this is the toughest one) you're getting the visitors that search for phrases in your comments (Google can't send those visitors to the other site as it doesn't contain the particular phrases) with the cross-domain canonical solution, as with the noindex solution nobody gets these visitors.