Question about the audio- I've listened repeatedly and it sounds like she's saying "et hey hatool" when I assumed it would be pronounced "et hahatool". She even seems to be combining the et and hay part then pausing before hatool. Am I hearing it funny. Is this some kind of linguistic quirk like when Vav becomes u' instead of v'?
Definitely yes. With a few exceptions - set phrases (few with ה before א, ח, ע, many with vav pronounced /u/; and in numbers of two+ digits where the last digit is 2 or 8; some 10% of the population (don't take the number seriously) will say 32 as /shloshim u-shtaim/, because it was hammered to us in kindergarten and early school. Interestingly, there's an exception to the exception: among these 10%, 90% including myself will say 112 as /me-a ve-shtem-esre/.
Is מוצה the equivalent of looking, as in "I am looking for my cat?"
it is possible to tell a story in active language like "so i keep having this dream, i go to the fridge for some milk, but i can't find any, and then i hear a weird noise and i find my cat dressed in a suit walking out the door, and he says he's going to buy milk..." XD just made that up but you get the idea. or "every day i find my cat hiding in the bathtub" could be another way of using it.
I agree with Avabelieve and the rest who said this sentence doesn't work in English. English would need something more, an object complement of some sort such as a prepositional phrase such as I find my cat in the water. It doesn't help to rephrase it as "I am finding my cat." It's an incomplete sentence or sentence fragment in English. I cannot say whether it works grammatically in Hebrew. I'm not worried about the matter. It would work in a different tense, future or past tense: I will find my cat or I found my cat.
The person you corrected wrote that to reply to the first comment by drewphil who made a mistake and wrote מוצה and esperanto1887 corrected him that find=מוצא not מוצה.
On another note. Even though correct, it's highly impractical to always list all four forms of a verb, so one is chosen, depending on which tense you need and usually masculine singular is listed only.
For all those that claimed the English was not natural, I can tastify that the Hebrew is just as unnatural. In future or past tense it's natural, not in present without saying anything else. In present it can work if it's repeated - כל שבוע אני מוצאת את החתול שלי בחצר אחרת. Same in English.
dandelionmagic invented a story in which the English can be used; in that context the Hebrew can be used, too.
It's definitely a strange sentence and will likely never be used, but in the broad sense, this course is teaching us to speak Hebrew, not regurgitate a few phrases one weekend. So whether or not these sentences are useful is up for debate, but the principles we are learning behind them are not. Thanks Duo!