A good example. Still it's only first and second that are irregular. The others have a bound to the initial number as of "three" with "third".
So it's just frustrating to learn tons of additional ways of counting to ten.. For people, for animals, for fish and so on and so on... why it's not allowed to just limit counting to the pieces?! :( very upsetting!
Not always the case, actualy not the case for most instances of counting. You'll find that "は" is primarily used as the pronounciation for "八" when counting eight things [for example; はっぱ (eight birds), はっびき (eight dogs), and most importantly - はっぱい (eight beers)]. "八" being pronounced "や" is more an exemption to the normal pronounciation, counters for "things" are in their own special category in Japanese for some reason.
Unfortunately, it's not that simple.
It would be either:
中 なか means "inside" in this context. It's used in its kun'yomi, its Japanese reading, here since it stands on its own without other kanji. Expressions of position at a location are added with a の behind the location.
So the structure is:
[location]の[position] (left, right, inside, outside, above, below etc.)
You have to use the counter word for cats here, which is 匹(ひき). It's used to count small animals in general. With most counter words the number is added directly in front of the kanji for the counter and read in its on'yomi, its Sino-Japanese reading. So that's why it's きゅう here.
If you write the number plus counter before the noun, a の is added between the noun and the counter since the counter acts like a noun in Japanese (like in the second sentence).
You can also add the number plus counter after the noun and its governing particle, like in the first sentence. Note that there is no additional particle behind the counter since the connection to the thing being counted is clear and the function of the counted thing is given through the particle が right behind it.
Furthermore, for animated beings います is used instead of あります.
On a side note, あります is written without kanji most of the time.
It is translated as that since it can be used for counting things which have no counter word or whose counter word is seldom used. In other cases, you would use the number without the added つ behind the kanji while reading the kanji in its Sino-Japanese reading and adding the fitting counter word behind the kanji for the number.