There are non verbal cues or different nuances in inflection that help disambiguate. There's also situational context.

Furthermore, people use simpler language when speaking then when writing.

In Chinese, which has even more homophones, it is quite difficult to tease out the meaning of a passage written phonetically (in hanyu pinyin). When speaking and there is a word out of context (such as a name), it is necessary to explicitly disambiguate by putting the word in a common phrase or describing the characters constituent parts. For instance, I would introduce my self as "Zhe as in 'philosophy', Hao which is 'sun' on top of 'sky'".

It's actually not uncommon when speaking to have to either draw a kanji in the air, or refer to the symbol you mean by cross-referencing another word that uses it to disambiguate.

No, but that's spoken Japanese. Different phrases are prevalent between spoken and written Japanese, as a workaround for those ambiguities.