(a) Two major shortcomings of Mendeleev's periodic table:
(i) Isotopes position was not confirmed
(ii) Position of hydrogen was doubtful
These anomalies were removed in modern periodic table:
(i) Isotopes were placed with their atoms, as all of them have same atomic numbers.
(ii) Hydrogen was assigned a position at the top of the period which is different but its nature matches with the group elements.
(b) Electronic configuration of X = 2, 8, 2 and Y = 2, 8, 6.
Both of them belong to the third period of the modern periodic table because three shells available in both of them.
To achieve noble gas configuration X will lose electrons while Y will gain electrons. So, they will form an ionic bond.
(c) X has two valence electrons so it comes under alkaline earth metal family (1) and Y has 6 valence electrons so it comes under oxygen family (16).
(d) Electronic configuration of X resembles magnesium (Mg) while the electronic configuration of Y resembles sulphur (S). So the ionic compound formed will be of XY type i.e. MgS.