Among the most widely used writing systems in the world, Chinese characters (Hanzi) - in their simplified variant as used in mainland China - have the highest graphical density.
So to ensure that a UI is CJK enabled, the Chinese character set is the 'golden constraint' you want to design to, as a font size and line spacing capable of displaying Hanzi will accommodate most other writing systems, including Devanagari and certainly Hebrew and Arabic.
Japanese uses some Chinese characters (Kanji = Hanzi), whereas Korean - though also Chinese inspired - is broadly an alphabetical script with grapheme-phoneme correlation... unlike Chinese, which correlates graphemes (i.e. distinct characters) to morphemes (simplistically speaking, minimal grammatical building blocks). The last bit is not trivial - it leads to lower overall character count in each sentence (most Chinese words are spelled with just two characters ).
Typically, and I've had native speakers / readers confirm this, the most common Hanzi characters require a 16 x 16 pixel minimum bounding box to display at a discernible resolution.
A good if perhaps inexact test is to pick a Wikipedia article that has a Chinese version - the language tag is 'zh' - toggle that to Chinese and isolate a few lines of text with Photoshop or a similar tool. Draw bounding boxes around numerous characters; you will find they do not always sit 'square' in the bounding box but will leave 1 or 2 pixel rows on top, left, right, or bottom unused.
Native Chinese speakers have also pointed out an interesting cultural typography tidbit to me: Most people who have grown up with the Hanzi writing system are used to discerning much subtler differences among characters displayed or printed with much higher graphical densities than are commonly found in Western (alphabet type) body text. One look at Chinese print media or even genuinely Chinese websites will give you a sense that there is a lower perceived need for whitespace than on a Western equivalent. Another good example are Apple user manuals, which tend to use fairly small Hanzi, often in hairline weight (!) with the end result that the Chinese text consumes about the same amount of space as Western text.
Another good resource is Google's Noto font project, one of the objectives of which is to create a global, universal font that addresses some of the uncertainties you mention in your question. The name comes from 'No Tofu', which refers to the portrait-oriented white-fill rectangles - like tofu, only inedible - that some browsers display when body text comprises multiple scripts, but whichever 'foreign' character set does not load. Interestingly, the Chinese Noto has five or six (if memory serves) stroke weight variants, covering a range from bold to hairline.
For accessibility reasons I would go bigger than the 16 x 16 pixel bounding box for Chinese. The 24 x 24 px size you mention should be a good base; with that, and appropriately adjusted line spacing you'll be able to display most other character sets of the world without any particular one looking excessively huge.
