How are Latin botanical names (e.g. Rattus rattus or Eucalyptus marginata) handled in Chinese? Does a Chinese botanist simply use Latin? Are there specific characters allocated for these words?
I'm native, but not a botanist.
For official binomial names, they are always Latin. We do have Chinese translation for every genus and species (well, at least most of the species), but not used in binomial names. These kind of translation don't use special characters, and usually not translated by sound, but by meaning.
It seems they use both. On this site, alternativehealing.com, there is a long list of botanical names, the characters and the pinyin as well. For completeness, I must say that in the Chinese wikipedia for "botanical names", 學名 (植物), it's stated that Latin must be used for classes, see the part titled "學名來源".
On the same site, in this page, there is even a dictionary; you can look up by the Latin name, the pinyin or the number of strokes of the characters (if you don't know the pinyin but you know the character).
all sciences done in chinese speaking country/regions basically all use english when it comes to technical lingoes. For chinese medicine/herb communities, if they are scientific (e.g. research, done university work) it's just english. Those traditional chinese herb community use the traditional names, but they are basically ignorant of modern botanical science. (e.g. it's this group that believes in rhino horns or tiger penis as aphrodisiacs etc.)