(i) When the elements having similar chemical properties are repeated at a regular interval, this is known as periodicity of elements. In modern periodic table (which is based on atomic number), we see that the elements having similar chemical properties are repeated at a certain interval of atomic number.
(ii) This is because the elements of same group have same number of valence electrons or they have similar electronic configuration. For example, all alkali metals (like sodium, potassium, etc.) have 1 valence electron.
(iii) The tendency to gain electrons across a period from left to rightincreases. This is because the effective nuclear charge increases and consequently it becomes easier for the atoms to gain electrons.