Words like 'manga' or 'anime' come from Japanese (written in kanji) or Greek words like onomatopoeia (Greek is a different alphabet from Latin) are ones that come to mind.
I realize my question was asking for examples of loanwords, but my intention was to ask for loanwords that also adapt the "foreign pronunciation and foreign spelling".
I am well aware that English borrowed plenty of words originating from non-Latin scripts, however based on your phrasing I thought you are saying something more than that is going on.
When a word is borrowed from a non-Latin script into English what else could happen other than adapting/borrowing the foreign pronunciation+spelling into English as well?