Earlier quoted context omitted.
Peking == Beijing. It’s the more phonetic translation of the mandarin name for the city.
No, Peking is not more phonetic than Beijing, and it isn't even Wade-Giles. Beijing is the currently accepted western name. You could make a linguistic argument for Wade-Giles, but not for the postal romanization.
In the English language, probably. I'm not a native speaker of English and momentarily forgot that "Peking" is unusual (although – in my defense – the English Wikipedia page still has it). But in my native language (German) everything other than "Peking" would be highly unusual.