Acids don't react with acids because acids are proton donors. This means that an acid will donate a H+ ion to the substance with which it reacts. Since both acids will donate a H+ ion to each other,...
Yes, though it depends on the specific acid. As an example, hydrochloric acid and hypochlorous acid undergo a very dangerous reaction that produces chlorine gas and water. HCl + HClO --> Cl2 + H2O
A strong acid is defined as one which disassociates completely in water. Lactic acid does not completely disassociate in water, therefore it is catagorized as a weak acid.