In 1848 only which of these was independent?

There were three actually. There was the Republic of Vermont, the Republic of California, and the Republic of Texas (which is the most well known).

That was Texas. They seceded from Mexico and, for a short time, were independent people. Once America overcame their problem with accepting Texas (they didn't want to anger Mexico, since they still laid clame to the territory) they sent troops to Texas and provoked the Mexican people to attack them.

Hawaii was an independent nation before becoming a territory of the United States and later becoming a state.