все течет, все меняется

Technically it is 'течёт'. In Russian, the dots over 'ё' are often omitted in writing, but the pronunciation remains 'yo'. For learners, it's best to write the dots.

Yes, but usually in a reflective or introductory part of the email, not in the technical details. It adds a professional, philosophical touch.

The Greek philosopher Heraclitus. It was later translated into almost every major language.

Not at all. It's used among friends to discuss life changes, though it might sound a bit dramatic if used for something tiny.

'Меняется' is more common in this proverb and sounds more natural. 'Изменяется' is slightly more formal and often implies a more fundamental or structural change.

Not a direct slang version, but people might say 'Всё по-другому теперь' (Everything is different now) for a more casual vibe.

It is neutral. It can be used for positive changes (growth) or negative ones (decay).

No. 'Всё' here is a singular neuter pronoun meaning 'everything'. Using the plural 'меняются' would be grammatically incorrect.

Yes, many Russian rock and pop songs use this phrase to talk about time and lost love.

You can agree by saying 'Это точно' (That's for sure) or 'Такова жизнь' (That's life).