[MorganFreeman]

I must draw these correct lewis structures.

Nitric Oxide:

But why wouldn't the valence electrons on the N atom be: one above, one left, one bottom?

Sodium Cation:
This would be a Neon atom with 8 valence electrons, or 4 electron pairs.

Hydronium Ion:
I know this is a covalent species, but does anyone know why?

[Yggdrasil]

I must draw these correct lewis structures.

Nitric Oxide:

But why wouldn't the valence electrons on the N atom be: one above, one left, one bottom?

How many orbitals would NO have?  How many are involved in the bond with oxygen and how many are available for the lone electrons?

Sodium Cation:
This would be a Neon atom with 8 valence electrons, or 4 electron pairs.

Yes.  Na⁺ would have the same electronic structure as neon.

Hydronium Ion:
I know this is a covalent species, but does anyone know why?

H₃O⁺ must be more stable than H⁺.

[MorganFreeman]

On Nitric Oxide:
Couldn't this be an ionic compound? The nitrogen donates 2 electrons to oxygen, leaving N with +2 and O with -2, causing them to stick together?

Or is it covalent? The nitrogen has a full 1s and 2s orbital, and an halfway full 2p orbitals. The oxygen has the 1s and 2s full, and its p orbital is 4/6 full. Do 2 p orbitals from the nitrogen combine with 2 lone electron p orbitals to form the bonds? This would leave a lone pair on N from its 2s orbitals, and give O 2 lone pairs from it's 2s and one full P orbital.

Or did I get this wrong. I didn't think hybridization applies in this case.

On Hydronium Ion:
Earlier I stated that this compound is covalent, but isn't it actually ionic? There are 8 valence electrons, so each hydrogen donates an electron to the oxygen and they "stick", right?