I’d like to know what the process is to get the translation from Transifex to Joomla, i.e. how do I get the translation included in the language pack so that I can test it?
In principle, you do not have to do anything, it goes automatically via script in the Kunena project and will included in the next language package.
I'm not sure, when you scroll down in our download page and download from the nightly build the language package, whether it's always up to date for tests.
Does the translation need to be reviewed? Can I do that myself (since there is no other translator)?
Yes, in this case you are the translator and reviewer at the same time. You can edit your strings at all times.
Does a certain amount need to be translated first? Will untranslated strings appear in English?
Kunena offers the option "Use English On Missing Strings" in the configuration (is default setting). So it's no problem, when not all strings are translated.