4:12a Let it be known to the king that the Jews who came from you to us

We (excl.) want the king/chief to know that the Jews who came to us from where you (sing.) are
-or-
Your Majesty, ⌊there is a group of⌋ Jews who left your part/side of the kingdom to travel/journey here.

4:12b have returned to Jerusalem. And they are rebuilding that rebellious and wicked city,

have reached Jerusalem. They are rebuilding that evil city that rebels ⌊against kings/chiefs⌋.
-or-
⌊We (excl.) inform you that⌋ they are now in Jerusalem ⌊city⌋ and are rebuilding it. The people of Jerusalem have always disobeyed and rebelled ⌊against kings/rulers⌋.

4:12c restoring its walls, and repairing its foundations.

They are completing the city walls and are repairing the foundations.
-or-
They are about to finish building the wall ⌊around the city⌋ and are repairing foundations ⌊in it⌋.

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