Hydrogen bonding is all about the pulling the shared pair of electrons from bonded Hydrogen, making it Hδ+.Then this partially charged hydrogen is enough to polarise the neighbouring electrons and make a weak bond known as the hydrogen bond.
So all you need a highly electronegative atom to polarise the Hydrogen, Oxygen is more electronegative than Sulfur.
(Generally, these electronegative atoms includes only Fluorine, Oxygen, Nitrogen)
In the question, it is asked to write Constitutional Isomers, Cis-Trans isomerism is part stereoisomerism. You don't have to worry about that.
Although Elimination reactions generally lead to the most stable product in major quantity. So trans product will be major. But it can also give you the wrong product, you have to consider the stereochemistry of the reactants. In this question, it doesn't matter so you are good to go.
You can always draw the all the products in single reaction separated by plus sign until unless you don't have to show the mechanism, it can be messy to show every mechanism in a single chemical equation.
Check Chemspider.com
You can write it in this manner, but it looks weird. So try to make structures as you have drawn in Computerised Image.