The verb "to field" in the sense that you are using it, means to respond to a question, or a telephone call, or a request; or to deal with a difficult item
The terms originates with the games of cricket and baseball. In those games the fielder catches or picks up a batted ball, which is not always an easy thing to do, and returns it, usually by throwing it to another fielder.
The chief of police will now field questions from reporters.
"Hit" has various meanings. In your sentence it means " to arrive at or appear at, in,or on"
Let's hit the store while the mega sale on notebooks is going on.
It's time to hit the beach.
The game's over. Everbody hit the showers!