Or can anything be made a commodity?
No - only things that are homogeneous (all the same) subject to certain standards (e.g. sulfur content in oil, octane rating for gasoline, etc.) can be considered "commodities". One key aspect of commodities is lack of differentiation. Buying "sweet" (low-sulfur) crude from a commodity exchange should be roughly the same oil regardless of who produced it.
For example, cell phones cannot be considered a "commodity" - there are differences in features, styles, etc. that make them heterogeneous and not classified as a "commodity".
Like, what about iron, salt, sheep, chicken, and so on?
Those could certainly be considered commodities, again subject to certain standards of characteristics. There may need to be additional
The reason you don't see these on a commodities exchange is likely because there's not enough liquidity (active buyers and sellers) to make it worth the effort of the exchange to provide trading services.
Where can I find a complete list of commodities?
If you mean commodities that are traded on an exchange, just get a list form each major exchange and consolidate the lists. If you mean "things that could be commodities", then there is no comprehensive list as anything that meets the definition of a commodity could be classified as a commodity. Wikipedia even lists DRAM chips as a "commodity" even though they aren't sold on an exchange, but I would disagree since there are certainly differences in quality and specifications from different chip makers.