Are all languages generate by Turing machines countable? Are all languages generate by Turing machines countable? I know that the set of all TMs are countable, but what about the languages that they generate?
Yes. All languages, not only those generated by Turing machines, are countable. This is because they are all subsets of $\Sigma^*$, and $\Sigma^*$ itself is countable. However, there are uncountably many languages.