We hyphenate the two words when they occur together to form one adjective "ill-mannered".

Is ill-mannered one word?

having bad or poor manners; impolite; discourteous; rude.

Is ill defined hyphenated?

The words "ill" and "well" are hyphenated when used with other words, such as ill-defined, well-chosen, well-known, to modify a noun. EXAMPLE The patient sustained an ill-defined injury to the shoulder. The parameters were ill defined.