Are these sentences natural?
I came across a shop that was selling novelties.
I happened across a shop that was selling novelties.
I happened to come across a shop that was selling novelties.

Question

Are these sentences natural?
I came across a shop that was selling novelties. 
I happened across a shop that was selling novelties. 
I happened to come across a shop that was selling novelties.

Answer

Yes, all three of these sentences are natural.  The first one is probably the most common and informal.

Answer

1st and 3rd seems fine but i am not sure about the correctness of the second point!!! :) trust it clarifies