I will try to explain how I interpret this reading. 'Certainly we will, said Galucon' is one of two sentences to be joined by a conjunction, 'and'. The semi-colon is used because there are a plethora of commas in the rest of this sentence. 'and with him Adeimantus, Glaucon's brother, Niceratus, the son of Nicias, and several others who had been at the procession.' In parallel construction of prepositional phrases, each qualified name is set off with commas (because you can take out the qualifiers such as 'brother' or 'son' and still have a valid sentence structure. So 'Niceratus, the son of Nicias,' also includes a comma after 'Niceratus' which wasn't noted in your quote.
The him refers back to the name, Polemarchus. The name Polemarchus appears before that of the other listed men in the main sentence joined by the conjunction, and. The third comma used confirms this fact. In order to discover 'who else', one would have to read about the 'procession', most probably. Maybe these names were listed previously in the historical passage when the procession occurred. It is understood that the verb 'appeared' applies to the whole sentence. 'And with him' and 'several others' would be diagrammed and joined by the conjunction 'and' under the main idea, Polemarchus appeared. 'And with him...' is a prepositional phrase that follows the 'understood' verb, appeared. I hope this explanation makes more sense to you.