The errors are:

- "wenting" -> "went" (wrong tense)
- "buyed" -> "bought" (irregular conjugation)
- "an apples" -> "an apple" or "apples" (illegal article / count pair)
- "goed" -> "went" (irregular conjugation)
- "a Apple" -> "an apple" (wrong article + case)
- "an very" -> "a very big" (wrong article + adverb preceding noun)

The fixed sentence is:

"He went to the store and he bought an apple. He then went back home and ate an apple with a very big smile"

We can apply further changes to make the sentence "flow" better

"He went to the store and bought an apple, then went back home and ate it with a huge smile."

But this slightly alters the meaning (he could have bought/eaten different apples) and even the originally-fixed sentence is grammatically correct.
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