When determining whether a molecule is aromatic, it is important to understand that aromatic molecules are the most stable, followed by molecules that are non-aromatic, followed by molecules that are antiaromatic (the least stable). Therefore, if it is possible that a molecule can achieve a greater stability through switching the hybridization of one of its substituent atoms, it will do this.

An aromatic must follow four basic criteria: it must be  a ring  planar,  have a continuous chain of unhybridized p orbitals (a series of sp²-hybridized atoms forming a conjugated  system), and  have an odd number of delocalized electron pairs in the  system. Furan is planar ring (fulfilling criteria  and , and its oxygen atom has a choice of being sp³-hybridized or sp²-hybridized. Depending on what hybridization the oxygen atom chooses will determine whether the molecule is aromatic or not.

If the oxygen is sp³-hybridized, the molecule will not have a continuous chain of unhybridized p orbitals, and will not be considered aromatic (it will be non-aromatic). If the oxygen is sp²-hybridized, it will fulfill criterion . Placing one of its lone pairs into the unhybridized p orbital will add two more electrons into the conjugated system, bringing the total number of  electrons to  (or, it will have  pairs of  electrons). Because it has an odd number of delocalized electrons it fulfills criterion , and therefore the molecule will be considered aromatic.

Because an aromatic molecule is more stable than a non-aromatic molecule, and by switching the hybridization of the oxygen atom the molecule can achieve aromaticity, a furan molecule will be considered an aromatic molecule.

An aromatic must follow four basic criteria: it must be  a ring  planar,  have a continuous chain of unhybridized p orbitals (a series of sp²-hybridized atoms forming a conjugated  system), and  have an odd number of delocalized electron pairs in the  system. This molecule cannot be considered aromatic because this sp³ carbon cannot switch its hybridization (it has no lone pairs). Therefore, it fails to follow criterion  and is not considered an aromatic molecule. It is a non-aromatic molecule.

An aromatic must follow four basic criteria: it must be  a ring  planar,  have a continuous chain of unhybridized p orbitals (a series of sp²-hybridized atoms forming a conjugated  system), and  have an odd number of delocalized electron pairs in the  system. If the molecule fails any of the first three criteria, it is considered non-aromatic, and if it fails the only the fourth criterion (it has an even number of delocalized electron pairs), the molecule is considered antiaromatic. In the case of cyclobutadiene, by virtue of its structure follows criteria  and . However, it violates criterion  by having two (an even number) of delocalized electron pairs. Although it's possible that a molecule can try to escape from being antiaromatic by contorting its 3D shape so it is not planar, cyclobutadiene is too small to do this effectively. Therefore, cyclobutadiene is considered antiaromatic.

There is no p orbital surrounding the Boron atom, so the ring does not have a fully conjugated pi system. In addition, there are 8  electrons, which does not follow Huckel's rule (an aromatic system contains 4n+2 electrons). The pi electrons include the lone pair (not shown, but implicit) on the nitrogen atom, which is why the answers with "6 electrons" are not correct.

The lone pairs on the two nitrogen atoms reside in sp2 orbitals, meaning they do not participate in resonance. Within the ring, there are three  bonds, meaning there are six  electrons. Thus, the molecule is aromatic because it is planar and follows Huckel's rule. 

Aldehydes are carbonyls with one R-group and one hydrogen attached to the carbonyl carbon.

Ketones are carbonyls with two R-groups attached the the carbonyl carbon.

This is an acid halide, were X is any halogen (group VII). They are the most reactive of all the carboxylic acid derivatives.

Carboxylic acids are composed of one R goup and a hydroxy group bound to the carbonyl carbon. The hydroxyl group gives the molecule acidic properties.

This is a hemiketal. Hemiketals are formed from the reaction of a ketone with an alcohol. The alcohol attacks the carbonyl carbon, reducing the double bond and adding a hydroxyl group.