No. Modern Japanese is the standardization of a 3 different scripts. Kanji, which are Chinese characters, katakana, which is a phonetic script made by simplifying Chinese, and hiragana. Katakana and kanji were used for official writing, and hiragana was used for informal writing. The Japanese government standardized the three scripts in 1915-ish and now they're all used together for different things.^
2. How do they manage to talk to each other, then?
Context, context, context. You can tell which homophone means what depending on the context and part of a sentence a word falls in. Sentences frequently consist of just the verb. Where we might say "turn it on" a Jap would say "on". Also Japanese people rarely interact with people outside their circle of friends/business acquaintances, and when they do it's in extremely formal circumstances where everybody knows what to say.
^Generally, katakana = foreign words, kanji = nouns/verbs, hiragana = grammatical markers(particles & verb conjugations)