Barium oxide has the formula #"BaO"#. It's an ionic compound, so its formula represents the lowest whole number ratio of elements in the compound. So #"Ba"_2"O"_2"# should be reduced to #"BaO"#.
Lead (II) phosphate
The formula for the lead (II) ion is #"Pb"^(2+)"#. The formula for the phosphate ion is #"PO"_4^(3-)"#. An ionic compound is neutral, so the total positive charge must be equal to the total negative charge. An easy way to determine the formula unit of an ionic compound is to use the crisscross method, where the size of each ion becomes the subscript of the oppositely charged ion. So the correct formula for lead (II) phosphate is #"Pb"_3"(PO"_4)_2"#.
Notice that when there is more than one polyatomic ion in the formula, it is placed inside parentheses and its subscript is written outside of the parentheses.
Nickel (III) sulphate is the correct name for #"Ni"_2"(SO"_4)_3"#
