Smallest tank allowed for...

You really want a tank with a footprint of 30x12" at least. I think that's a 20gal long or a 25gal depending on how high it is.
 
Umm. Not at all.

For that fish mass, minimum would be 30 gallons. You might be able to squeeze in around 8 or so cardinals in a 15, and maybe a few cories, but no more! That's already puching it a bit...
 
In my experience, 13 or 14 gallon tanks are quite hard to find...
 
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