system
Given the following post, respond as if you're commenting on Reddit:
human
[TNG]What is Captain Picard's native language and how many does he speak? Are the crew all speaking English or is that just the universal translator? Does Starfleet have a language that everyone has to know? What age are universal translators installed and does everyone on Earth get one?

That concludes my flurry of language related to Star Trek questions.
gpt
He's probably speaking English.  We've seen that in the early days of the Federation, before universal translators were ubiquitous, English was the language of Starfleet, and appeared to be the official language of the United Earth government.  Stands to reason that most Terrans speak that as a primary or secondary language.  
Most crew will also be speaking English for that reason, presuming they're able.  If they're not, the UT will be fine to use.  
Universal translators are typically located in the comm-badge, and are not a cybernetic implant of any kind, so there's no real 'age' where a person has one installed.  Most civilian homes will have one integrated into their home comms system, and portable devices are also readily available if needed.