Here "hand" refers to God's power which he would use to punish his people. Alternate translation: "I will begin to use all my power against you" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Here the process in which God removes his people's sin is spoken of as if her were separating metal from the bad things mixed with it. The words "as with lye" adds another metaphor, because lye is used in soap, not in refining metal. Alternate translation: "and like fire removing the dirt from silver, I will remove all the evil from among you" (See: [[rc://en/ta/man/translate/figs-metaphor]])