(a) Two criteria used by Mendeleev in creating his periodic table:
(i)Mendeleev's periodic table was based on the observation that the properties of elements are the function of their atomic masses. This means that if elements are arranged in the increasing order of their atomic masses, then their properties get repeated after regular intervals.
(ii) Relative atomic mass and similarity of chemical properties.
(b) Mendeleev's periodic law states that the physical and chemical properties of elements are the periodic function of their atomic weights.
(c) hydrogen has atomic mass 1 so definitely, it must be in the first period but the group was confusing. He found that hydrogen forms oxides like alkali earth metals with formula H2O as Na2O. He also found that hydrogen is similar to halogens in forming diatomic molecules H2 like Cl2, Br2. So, he could not assign a fixed position to hydrogen.
(i) On moving left to right in a period, atomic size decreases because of the number of electron increases due to which attractive forces towards nucleus increases and atomic size decreases.
(ii) On moving down the group, atomic size increases due to the increase in valence shells.