Are there concrete rules of conversion between "homophone" English and Chinese proper names?
Yes and no. It's a very broad subject as there are many different varieties of spoken Chinese, there are different methods of transliteration, and the rules themselves have been in flux at various times in history.

I'll just address your examples, but realise that there are many more cases and rules not covered.


  Australia : 澳大利亚 ( Àodàlìyǎ )


This name originated during a time when English -> Chinese transliteration was in its infancy and no hard rules existed. People just picked whatever characters sounded close and easy. For Australia in particular, the transliteration probably came from European missionaries, who preferred using phonetics rather than the usual Chinese preference for using single character + type, you know like 英国 or 欧洲. There's more details here: http://www.qinshuroads.org/Chinese_Australia/Oz_Name_dj.htm


  John : 约翰 ( Yuēhàn )


Again, missionaries most likely. "John" is pronounced "Yohann" or "Yohanna" in many languages.


  Singapore : 新加坡 ( Xīnjiāpō )


A bit more complex. Singapore is originally a Sanskrit name, so you're comparing two different transliterations. It's why its name resembles many Indian city names. By luck they are still similar, but it's not always the case as we'll see later...


  Hong Kong : 香港 ( Xiānggǎng )


These are not terribly similar, but that's because the English name is derived from Cantonese instead, which is pronounced Heong Gong.


  Peter : 彼得 ( Bǐdé )


Missionaries.


  Japan : 日本 ( Rìběn )


This is one of my favourites. They are the same name. Basically Portuguese got the name from Wu Chinese, for some reason, as Cipan. Meanwhile, the Dutch got the name but via Southern China, as Yatpun, which they wrote down as Ja-Pun because J sounds like Y in Dutch. Of course, neither of these routes involved Mandarin, which has its own somewhat different pronunciation.


  America : 美国 ( Měiguó )


Another interesting case. This name was settled on after a very long period of evolution, over a time where basically the Chinese had no idea how to properly transliterate European names. Note that the proper, full name for United States of America is 美利坚合众国, and 美国 is an abbreviation. But if you thought there were too many names for America, wait 'till you see how the Chinese tried to translate "President". The concept of a paramount leader that is periodically overthrown by non-nobles was really baffling. There were variants from "big leader", to complete phonetics (pu-rui-si-deng-te), to weird hybrids "伯里玺天地" (hey there, snuck in 玺 and 天地, both implying Emperor). Sinologist Jonathan Spence explores this subject in more detail.

All your examples are either complex cases or historical examples where no rules existed. That's different now, to prevent every new foreign word producing dozens of Chinese translations. Here are some related questions:


Why do Chinese translations of English names sound very inaccurate?
How do we know what characters correspond to Chinese names?
How does foreign word transliteration work in the context of Cantonese vs Mandarin?