1. Phenol can refer to the actual compound (C6H5OH) or compounds with a phenolic functional group. So yes, phenols can be considered a homologous series. The functional group is an alcohol (-OH) on an aromatic ring.
2. You should take the functional group which encompasses the most functional groups. For example, you should not consider a carboxylic acid an alcohol or a ketone even though it contains an -OH and a carbonyl group. In chemistry, the whole is more than the sum of its parts. A carboxylic acid has different properties than the combination of a ketone and an alcohol. For example, a carboxylic acid has an acidic proton where neither an alcohol nor a ketone contains any significantly acidic protons. Similarly, a phenol is contains both an alcohol functional and an aromatic functional group. Together, these two functional groups give phenols different properties than both alcohols and aromatics. For example, the OH on the phenol has a relatively low pKa (~9-10 vs. ~13-14 for an alcohol).
3. I would consider this an aromatic hydrocarbon. In general, if an alkane has any functional groups attached, you would not consider it an alkane, unless the alkane is very long (for example, in fatty acids).