How does a virus live can they exist on their own?

Answer 1

Without a host cell a virus is not exactly alive.

But yes, viruses can exist alone but they do nothing. However many viruses are fragile and breakdown on exposure to air, others can remain for years on a surface just waiting for a host to infect.

Answer 2

Yes, until it parasitises a living cell a virus is just a tiny inert "crystalline" piece of protein and nucleic acid.