Ellipsis

They have sold their house and … on a tour of the world.

(a) go
(b) went
© gone
(d) going

Question ¹ 1
My friend told me that "going" would be correct.

But my version is © . Am I right?

Question ¹ 2 

Can I say:

 They have sold their house and [b]have[/b] gone on a tour of the world.

Is the auxiliary "have" optional here?
  1. You are right.

  2. Yes, it is optional.