China and Taiwan have/had telegraph codes. Each character has a corresponding number. Components of characters do as well, so even though I could just send the character for 仁 (code 0088), maybe instead I send 亻 (0086) and 二 (0059) separately, or if it's a complex character maybe I know the components by heart whereas I'd need to look up the code for the single character, so I transmit the components in order and the guy on the other end has no trouble putting them together. A competent user would know the codes for the more basic characters by memory, as well as the components. In other words you're not having to look up every character every time.
Taiwan and China had the same basic system (same numbers) but a few glyphs are used in one place and not the other so you might find outliers that way.
There's a wikipedia page that has more on this if you're interested.
Arabic is still an alphabet though so there's no reason why an equivalent Morse-style code couldn't exist.
Further reading:
Korean used a system called Standard Korean Alphabet Transliteration System (SKATS). It is not a true transliteration system, even though that's in the name, instead it takes advantage of equivalences between Korean Morse code and Morse code.
So for the word 한글 (hangul), it is broken up into its constituent letters ㅎ ㅏ ㄴ ㄱ ㅡ ㄹ. Korean Morse code for ㅎ is .---, which would also be J in Morse code. Following this pattern you could then write 한글 as JEFLDV.
It is important to remember that despite being written in Latin script you can't read the word in anything other than Korean.
I don't know of any academic sources on this subject, but there is a Wikipedia page: https://en.wikipedia.org/wiki/SKATS.
SKATS is still taught as part of the Korean curriculum at the Defense Language Institute in Monterey, CA.