is this always true that the compound NH3 contains two double covalent bonds? and that the chemical formulas of molecular compounds show the number and type of atoms in each molecule.

No. NH3 has no double bonds. It contains three covalent bonds, one covalent bond for each H attached to the N. It is true that chemical formulae show the number and kind (perhaps kind is a better word than type) of atoms in each molecule.

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