Judaism obviously does not give any validity to superstitions of the Western culture.
However, I did hear something re opening an umbrella in a home – is there a Torah source for this.
Answer:
As you rightly note, halachah does not give any credence to superstitions (such as touching wood, black cats, and so on), and doing so possibly involves a transgression of the obligation of tamim tihiyeh. See here for an article on this topic.
I have not heard of an exception to the rule with regard to opening an unbrella at home (though it is not advisable for practical reasons).