What is a polite term of address to use for a friend's mother?
Is it impolite to call her by name?
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In order to address my own mother, I would use the word "어머니."
In order to address someone else's mother, I would use the word "어머님." It comes down to honorific usage; please refer to the section Honorific nouns in the Wikipedia entry on Korean honorifics.
It is never polite to call anyone by their names unless they are of the same age and your friends.
You can't use '씨' after their names, either as it sounds disrespectful.
As suggested by @PhonicsTheHedgehog, it is better to use '어머니' or '어머님' which is an honorific form of '엄마 (mother)' which is used to call your own mother.
If you are close enough to her, you can call her '엄마', but it is rare. If you are not close enough to call her '어머님' or '어머니', you can call her 'your friend's name + 어머니 (어머님)', for example, 철수 어머니 (어머님). But it could sound too formal if you use 철수 어머님 which is more broadly used by 철수's teacher, for example.
I have never heard anyone calling their friend's mother '아주머니' or '아줌마' as they are used to call an older woman you don't know, for example a woman in their 40's and 50's who are working in a restaurant or selling things in the market.
It is not easy to decide which to use, but you can stick to 어머니 and 어머님 as no mother will take offense from them and rather they would like it.