Hiwa.

Anak, pakihiwa ang mga gulay kasi magluluto ako ng yung pinakbet. - “Kaya”, in this case, translates to “that's why”.  "Kasi" is "because".  “Yung” (that) shouldn't be there.

Hiniwa sa apat ng Tita ko ang mansanas para sa iyo - Correct! It's just that it should be “ng tita ko”. If you are using “Tita” as a name or an appellation, then it should be “ni Tita”, without the “ko”, unless you want to emphasize that she is the “Tita” that you “own”, e.g., your wife or daughter, and not to be confused with another having that same name.

BTW, I forgot to mention that the reason why you should use “ang” and not “ng” was because your sentence was object-focused.

Object-focused: (HiwaIN)

PAKIHIWA ANG mga gulay = Please cut the vegetables (It may actually be said as "pakihiwain", but we almost always just say "pakihiwa").

HIWAIN mo ANG mga gulay = Cut the vegetables

Subject-focused: (MAGhiwa) 

Pwede bang MAGHIWA ka NG mga gulay? = Can you (please) cut some vegetables?

MAGHIWA ka NG mga gulay = Cut some vegetables.