From my understanding hydrogen peroxide only reacts with bacteria in a way that it should burn them more or less.
If that is true, can I then safely use hydrogen peroxide to clean my bathroom sink which are made of porcelain?
While hydrogen peroxide is not normally used for cleaning surfaces, there is nothing in normal glazed porcelain that it would damage. Porcelain is about as unreactive to most things as glass, which is unreactive enough to be used for the bottles that store hydrogen peroxide.
But you should probably be careful with it as it can be dangerous if the solution is a strong one. Normally available hydrogen peroxide should not be as strong as the solutions used in the lab, though, which is often a 30% solution in water and should only be handled if you know what you are doing (see the safety data sheet). Consumer hydrogen peroxide is usually a 3-6% solution and isn't any more dangerous that hypochlorite bleach (and is a safer way to bleach hair).
Standard household (hypochlorite) bleach is usually better for cleaning, though.