And here we go again - not using nikud counts as a typo.
Can this be used in an analogous way, such as "He does not acknowledge you"?
In that case, is "He is not looking at you." wrong?
It almost seems like there's a r sound in אותךָ like it's "ootrah" but isn't that a caf sofit? I'd have read it "ootreca" or something if it wasn't for this recording. Is there something I'm missing here or is this just an irregular pronunciation?
It's the soft pronunciation of כ, which in modern Hebrew is just like ח, and indeed may sound similar to ר, depending on your "mother ear". For Hebrew speakers they are clearly distinct sounds.
Why don't we say הוא לא רואֶה אתְּ?
Pretty much like in English you say "he sees her" and not "he sees she". Linguists call this nominative vs. accusative; in modern English, by accident, they are the same for "you".
In this context is "you" masculine or feminine?
Masculine. Feminine would be /otach/.