A hydrogen bond is not a proper chemical bond, but the result of dipole-dipole interactions. While they are very chemically important, hydrogen bonds are dynamic, rather than stagnant. This is the least stable type of bond listed.

Covalent bonds are inherently more stable than ionic bonds as electrons are shared between both bound atoms, so the next stronges bond type is the ionic bond.

Chemists distinguish between covalent and ionic bonds for the sake of simplicity, but there is actually a continuum. Polar covalent bonds are on the continuum between pure ionic bonds and pure covalent bonds, so polar covalent bonds have more ionic character than nonpolar covalent bonds, and thus are less stable than nonpolar covalent bonds.

IMF strength is in the order of ion-ion>h-bond>dipole-dipole>van der waals. Of the listed compounds there aren't any that display ion-ion IMF, and only ammonia has h-bonding, making it the one with the strongest forces.

Helium gas will have the lowest boiling point since it is a noble gas and the only intermolecular forces present are dispersion forces, which are the weakest. Acetone has a dipole, so dipole-dipole forces will be present. Water has a dipole and can also hydrogen bond, as can isobutyl alcohol. However, isobutyl alcohol is heavier than water, and will thus have the highest boiling point.

LiOH displays ion-dipole IMF, H_2O displays hydrogen bonding, and CO₂ displays dipole-dipole. Ion-dipole is greater than hydrogen bonding as an IMf, and hydrogen bonding is greater than dipole-dipole.

Ion-dipole forces are the forces responsible for the solvation of ionic compounds in aqueous solutions, and are the strongest of the intermolecular foces. Hydrogen bonding is the second strongest intermolecular force, followed by dipole-dipole interactions. London dispersion forces are present in all solutions, but are very small and the weakest of the intermolecular forces.

Noble gases are uncharged and do not have polar covalent bonds or dipole moments. The only force that could apply to them are dispersion forces.

The choice "The slightly negatively charged sulfur atoms in are attracted to the slightly positively charged  hydrogen atom of a nearby molecule" is exactly analogous to hydrogen bonding in water.

"Two methane molecules are attracted to one another because of temporary dipoles" describes London dispersion forces.

While "A negatively charged chlorine anion in solution will attract nearby positively charged Lithium cations" may sound like hydrogen bonding, it is more descriptive of  interactions between any charged particles, not charged particles within the same molecule.

"Water completely dissolves certain salts, like " does not describe bonding at all.

While "The chlorine bound to carbon in dichloromethane will slightly attract positive charged particles" sounds promising, the slight charges are not on the same molecule.

Methanol is not an ionic molecule and will not exhibit intermolecular ionic bonding.

Methanol is polar, and will exhibit dipole interactions. It also contains the -OH alcohol group which will allow for hydrogen bonding.

Dipole-ion interactions (an attraction between an ion and a neutral, but polar atom) are the strongest intermolecular forces listed. Ion-ion forces (attraction between two ions) are the strongest interactions overall.

Hydrogen bonding, an attraction between a hydrogen atom and a highly electronegative atom like fluorine, oxygen, or nitrogen, is the second strongest interaction listed.

The third strongest listed is dipole-dipole interactions, an attraction between two polar molecules, followed by dispersion forces, temporary shifts in the electrons of a molecule.

Hydrogen bonding is what holds the hydrogen in one molecule of water to the oxygen in another molecule. Surface tension is a measure of the difficulty to disturb the surface of a liquid. The strong intermolecular connections created by hydrogen bonding makes it hard to disrupt adjacent molecules and break the water surface.

Most key properties of water are attributed to its hydrogen bonding.