The classic biochemical way to do this would be isotopic labelling. You grow virus host cells in media with funny isotopes of carbon, nitrogen, phosphorous, wha

The classic biochemical way to do this would be isotopic labelling. You grow virus host cells in media with funny isotopes of carbon, nitrogen, phosphorous, whatever you like, use those to produce virions, feed the virions to Halteria growing in an isotopically normal environment, wait a while, then collect the Halteria, separate them into their component molecules, and use mass spectrometry to see which ones have funny isotopes in. This doesn't entirely answer all the questions you posed, but it does definitively tell you whether the Halteria are incorporating material from the virions into themselves.