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It is mandatory to install it, even on an Asian computer.
The chosen font must contain the characters that are to be displayed. It can be checked with the Character map on Windows.
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Some foreign characters may have a larger vertical size than english ones, so if the characters have to be displayed in a table, the size of the cells must be set accordingly.
There is a known issue within Acrobat, dealing with listboxes and Chinese characters. Details can be found on the following page:
http://www.deskdr.com/dr/acrobat-pro-with-acroform-the-listbox-event-changeex-with-chinese-text-issue.html