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.

To determine the number and type of bonds in a compound, we need to look at the Lewis structure. In the case of NH3, ammonia, the Lewis structure shows that there is a central nitrogen atom bonded to three hydrogen atoms.

The Lewis structure for NH3:

H
|
N-H
|
H

In this structure, nitrogen forms three covalent bonds with three hydrogen atoms. Each covalent bond consists of a pair of electrons being shared between the atoms. There are no double bonds in NH3.

Regarding the chemical formulas of molecular compounds, they do indeed indicate the number and type of atoms in each molecule. For example, the chemical formula for water, H2O, tells us that each water molecule contains two hydrogen atoms and one oxygen atom.