Do brand hyzaar (losartan and hydrocholorthiazide) 100/12.5 and generic losartan hctz 100/12.5 work the same?

Yes, but not likely: Same drug.

Use of generic drug: Generic drugs are meant to be exactly duplicate the action of trade name drugs that have lost their patent protection. I would ask your doctor and i believe that he will tell you generics work as well as the branded drugs.

Yes: Yes, but there can be subtle differences but not usually significant ones.