Where is "I - אני" here? That lesson was very hard to me.
It's the same structure as יש לי in present tense. הייתה לי-- there was to me.
It is hidden in the pronoun לי, which is dative of אני.
Hayta li ke'ara aval hem lakchu ota.
This is tough. It seems like the translation should be "but they took it from me" no?
No, it is correct the way they have it: "I had a bowl but they took it." There is no "from me" (mimeni, ממני) in the sentence.
קערה = salad bowl