What is the position of metalloids in the periodic table?

$(a)$ Why do we classify elements?
$(b)$ What were the two criteria used by Mendeleev in creating his Periodic Table?
$(c)$ Why did Mendeleev leave some gaps in his Periodic Table?
$(d)$ In Mendeleev's Periodic Table,why was there no mention of noble gases like Helium,Neon,and Argon?
$(e)$ Would you place the two isotopes of chlorine,$Cl-35$ and $Cl-37$,in different slots because of their different atomic masses or in the same slot because their chemical properties are the same? Justify your answer.

An element $X$ belongs to the $3rd$ period and group $13$ of the Modern Periodic Table.
$(a)$ Determine the valence electrons and the valency of $X$.
$(b)$ Determine the molecular formula of the compound formed when $X$ reacts with an element $Y$ (atomic number $= 8$).
$(c)$ Write the name and formula of the compound formed when $X$ combines with chlorine.

An element $X$ of group $15$ exists as a diatomic molecule and combines with hydrogen at $773 \, K$ in the presence of a catalyst to form a compound,ammonia,which has a characteristic pungent smell.
$(a)$ Identify the element $X$. How many valence electrons does it have?
$(b)$ Draw the electron dot structure of the diatomic molecule of $X$. What type of bond is formed in it?
$(c)$ Draw the electron dot structure for ammonia and what type of bond is formed in it?

An element $X$ belongs to the $3rd$ period and group $16$ of the Modern Periodic Table.
$(a)$ Determine the number of valence electrons and the valency of $X$.
$(b)$ Write the molecular formula of the compound formed when $X$ reacts with hydrogen and draw its electron dot structure.
$(c)$ Name the element $X$ and state whether it is metallic or non-metallic.

Two elements $M$ and $N$ belong to group $I$ and $II$ respectively and are in the same period of the periodic table. How do the following properties of $M$ and $N$ vary:
$(a)$ sizes of their atoms?
$(b)$ their metallic characters?
$(c)$ their valencies in forming oxides?
$(d)$ formulae of their chlorides?