Słyszę vs. Słyszą?
Ja słyszę - I hear
Oni/One słyszą - They hear
Why is "kota" used instead of "kot"
"słyszeć" (to hear) takes Accusative, and the Accusative form of "kot" is "kota".
Why cant I omit "ja" in this sentence?
You can, it should have worked. Although in such an unsual construction, I would recommend leaving it here.