Así es la vida.

Not usually, but it can be if used to dismiss someone's serious feelings. Use it for shared inconveniences, not to shut someone up.

It's a bit informal for a first email to a client, but fine for internal chats with colleagues you know well.

In meaning, nothing. But 'Así es la vida' is what Spanish speakers actually say, whereas 'C'est la vie' is a French loanword.

Because we are talking about the nature of life itself, which is considered a permanent characteristic in this context.

Yes! That means 'That's my life' and is often used to talk about your own specific recurring problems.

It is used equally across the entire Spanish-speaking world. It's one of the most universal phrases.

You can just nod and say 'Sí, es verdad' or 'Ni modo'.

Yes, if someone is complaining about something very minor or 'first-world problems,' you can say it with a roll of the eyes.

Not of this specific phrase, but 'Ni modo' or 'En fin' serve similar purposes.

Not inherently, though it aligns with the idea of accepting God's will in religious contexts.