1.I was shown by Kate all the things she bought.
2.I was shown all the things she bought by Kate.
Which position is suitable for "by agent" in this passive voice?
1.I was shown by Kate all the things she bought.
2.I was shown all the things she bought by Kate.
Which position is suitable for "by agent" in this passive voice?
The natural place for the by-phrase in the passive sentence you gave as an example would be at the end, although the sentence is not clear to begin with, because of the pronoun she, mainly. Change it to they and it becomes a better example.
Kate showed me all they bought.
I was shown all they bought by Kate.
Kate showed me everything she (or they) bought. is how your sentence would normally be stated if there isn't a good reason to use the passive.
One possible reason for moving "by Kate" ahead of "all (the things) she bought" would be if the noun phrase is felt to be rather long and weighty:
... shown by Kate {all of the things she bought using the money she received for her birthday}.
Another would be when the by-phrase merits special emphasis, either to avoid a potential ambiguity or to shine a spotlight on the fact itself:
They were shown by the director himself the museum's latest acquisitions.
P.S. It is also grammatical to begin the sentence with the by-phrase:
By the director himself they were shown the museum's latest acquisitions.
but such sentences are found mainly in writing, not in colloquial speech.
The passive, if there is no good reason for its use, already sounds somewhat wooden; moving the by-phrase out of its usual position at the end of the sentence only makes things worse in that respect.