Is a fatty acid a polymer?
Fatty acids are usually not considered polymers.

From a biological viewpoint this is simply because there is only a very limited set of chain lengths that exists in nature (~2-20 or so) and also even numbered chains are much more common than uneven numbered ones. In contrast to this 'true' polymers can have an arbitrary length of chain length (of course there is still a limit in biology, but not a super strict one) and no specific lengths are favoured.

From a chemical viewpoint fatty acids are also not really a polymer: you can't just take a bunch of alkyl monomers and fuse them to one long fatty acid  chain, because simple alkyl monomers don't have chemical groups that allow this reaction to take place (making C-C bonds is chemically not the easiest thing to do).