Hello,
your first observation is definitely not a bug, it is just a common misconception when getting started.
You can use any card to make combos, not only cat cards, it's just that the cat cards have no other purpose except being combined.
The only exception here is that a feral cat can only be used to replace another cat in a combo, not other cards.
As for your second question with playing cards on yourself, it's not a bug either, there are definitely good reasons to do that depending on your strategy.
For instance, a commin useful item is to play a targetted attack on you, especially at the beginning of the game when you are least likely to draw an exploding kitten to draw more cards from the deck.
On the other hand, playing combos on yourself doesn't seem all that useful to me, but this game also has some additional card packs where it might be more useful in the future. Note that I am talking about the physical game itself, these extensions aren't available on the Playroom at this time.