A nonpolar covalent bond occurs when two atoms share electrons equally. This happens when the electronegativities of each atom is relatively close to one another. For example, in water, oxygen is much more electronegative than hydrogen (3.5 and 2.1 respectively), oxygen keeps the electrons closer to its nucleus and results in uneven sharing of the electrons between itself and the two hydrogen atoms. This results in a net dipole in the molecule with the oxygen-end being slightly negative, and the hydrogen-end being slightly positive.

The octet rule requires that each atom in the molecule has eight valence electrons, fully filling the s and p subshells. Atoms that have a full octet tend to be more stable and lower in energy.

In the compound , each fluorine has seven initial valence electrons and boron has three initial valence electrons. Upon forming the compound bonds, boron shares its three electrons with each fluorine through covalent bonds. This givens each fluorine a full octet, but leave boron with only three covalent bonds, resulting in only six valence electrons. Boron does not satisfy the octet rule in this compound.

Each atom in the other listed compounds forms bonds to generate a full octet. Sodium chloride achieves this through an ionic bond. Methanal and diatomic oxygen both use double bonds to help achieve octets.

..            ..

:F — B —  F:         Boron can have a violated octet (6 e^-) and each F has 3 lone pairs

..      |      ..          for a total of 9 pairs of unpaired electrons

        :F:

         .. 

BCl₃ only has six electrons around boron, while NO₂ (with an odd number of electrons) would have only 7 electrons around the central nitrogen.

Lewis dot diagrams can help us keep track on how the valence electrons will disperse themselves among orbitals in the atom. When drawing these diagrams, it is important to keep two things in mind.

1. The s orbital will be filled before the p orbital begins to be filled.

2. Electrons will never pair in the same orbital if an orbital of equal energy is unoccupied.

Knowing these two facts, we can predict which of the following elements will have two unpaired electrons.

Fluorine will have seven valence electrons, meaning that only one orbital will not be completely filled.

Beryllium only has two valence electrons, but they will both be found in the 2s orbital, because it must be filled before the p orbitals can receive electrons.

Nitrogen will have five valence electrons, so two will be found in the 2s orbital. The other three will be present in their own p orbitals, meaning nitrogen has three unpaired electrons.

Neon will have eight valence electrons, fully filling the 2s and 2p orbitals. It will have no unpaires electrons. 

Carbon has one less valence electron than nitrogen, meaning that it will have two unpaired electrons in the p orbitals.

Isoelectronic means having the same electron configuration (i.e. the same number of electrons).  and  both have the same number of electrons (18), while sulfur has 16, phosphorous has 15, neon has 10, and the sodium cation has 10.

When drawing a Lewis dot structure, we are always trying to reach an electron count where all atoms involved are stable and (usually) have full octets. We are also trying to estabilsh a structure in which we have the smallest formal charge possible. The general rule is first to draw out all of the elements involved and their valence electrons, then start piecing them together trying to reduce the formal charge and get all elements involved to an octet. There are a couple exceptions to the octet rule.  

Sodium and chlorine form an ionic bond, meaning that one atom will donate an electron and the other will receive it. This gives each atom a charge. Chlorine has seven valence electrons, while sodium has one valence electron. For each atom to arrive at an octet, sodium will need to lose one electron and chlorine will need to gain one electron. This would give chlorine a negative charge, and sodium a positive charge.

Thus, the answer is a sodium with a positive charge (due to one lost electron) and a chlorine with eight electrons and a negative charge (due to one electron gained). 

When drawing a Lewis dot structure, we are always trying to reach an electron count where all atoms involved are stable and (usually) have full octets. We are also trying to estabilsh a structure in which we have the smallest formal charge possible. The general rule is first to draw out all of the elements involved and their valence electrons, then start piecing them together trying to reduce the formal charge and get all elements involved to an octet. There are a couple exceptions to the octet rule.

In this case, boron actually has an incomplete octet. Though there are resonance forms in which boron has a full octet, when you calculate the formal charge of these configurations it will not be zero.

In an ammonia molecule, the nitrogen is bonded to three hydrogen atoms and also has a lone electron pair. This lone pair will repel the three hydrogens out of a planar orientation, which results in a trigonal pyramidal geometry.

Compounds with the general formula AX₃ and one lone pair will be trigonal pyramidal.

Compounds with the general formula AX₃ and no lone pairs will be trigonal planar.

Compounds with the general formula AX₄ and no lone pairs will be tetrahedral.

Compounds with the general formula AX₅ and no lone pairs will be trigonal bipyramidal.

Methane has a carbon atom attached to four hydrogen atoms. In order to be as far as possible from one another, the hydrogen atoms will orient themselves around the carbon in a tetrahedral geometry. Tetrahedral geometries have bond angles of  between each constituent.