Why is this so funny!!!!!!!?????????? ㅋㅋㅋㅋㅋㅋㅋㅋ

집으로 is "in the direction of home" but I think could be basically the same in this case.

집에 implies destination, while 집에로 implies direction. "I go home" implies destination, so the first one should be used.

저 is used to lower oneself while the ㅂ니다 verb endings are used to raise the other person. You can raise the other person without lowering yourself. However, it is kinda weird to lower yourself while not also raising the other person.