Is Saudi Arabia a kingdom?
Yes , it is the Kingdom of Saudi Arabia and is ruled by King Abdullah bin Abdul Aziz.
Saudi Arabia was never colonized, so it has always been independent. The modern Kingdom of Saudi Arabia was founded by the as-Saud Dynasty, which was ruling the Kingdom of Nejd. When Nejd conquered Hejaz, the Sauds decided to rename the unified kingdom as their kingdom, which is where the term "Saudi Arabia" comes from.