Is it true that all verbs have a corresponding noun form (which is formed by making the -masu form and removing the -masu)?
Like 遊び and 遊びます 飲み and 飲みます 生き and 生きます 死に and 死にます
For the most part, yes. There are a few outliers that don't though. Most 尊敬語 and 謙譲語 verbs don't form nouns with their 連用形. And some 連用形, such as 「なり」, are specialized almost to the point of uselessness.
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