Singular or plural for "cat"?

Question

I always have many confusions for singular or plural, should the cat be a cat, cats or simply cat:

Human adopted many pets in history, for example cat, dog, etc...

Human adopted cats in history.

What cat do you eat?

What kind of cats do you eat?

I just want to say a thing or a concept called "cat", it's unimportant wether there are many cats or not, but maybe "cat" should be regarded as a collected whole, so "cat" is inherently cats hence it should be cats?

The same for "kind" above.

BTW, I remember there are some special word combinations (maybe using prepositions?) that you don't need "s" after nor "a" before countable nouns, but I can't remember specific details, it would be really helpful that someone makes some such examples. (I assume "what" is one of the example?)

Answer 1

Some examples for you:

Humans adopted many pets in history; for example the cat, the dog, etc.
Humanity adopted many pets in history; for example cats, dogs, etc.

In these examples both "cats" and "the cat" represent the group of historical cats who were adopted, while "Humans" and "Humanity" represent the group of humans who adopted them.

Humans (have) adopted the cat throughout history.
Humanity has adopted the feline throughout history.
Humans have adopted cats throughout history.
Humanity has adopted many a cat throughout history.

In these examples "the cat" and "the feline" and "cats" all represents cats adopted during history, while "Humans" and "Humanity" represent the many people during history that adopted cats. The usage of "many a" in the last example, although not common usage, is an acceptable way to allow me to imply "cat" in that sentence is plural; it implies "many cats".