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Fluid statics or hydrostatics is the branch of fluid mechanics which deals with the study of fluids at rest and the pressure exerted by it on an immersed object. If your question is about the study of fluids in motion, use the tag "fluid-dynamics" instead.
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Can helium gas lift the bottle itself?
Yes. If something has a net density lower than air, it will float. If the circumstances result in a bottle with helium having a net density lower than air, it will float.