About the origin of the names "immune" and "simple"
I don't know the history, but "immune" always struck me as fairly appropriate terminology. ("Simple" never really did, but I never thought of the analogy with simple groups before - it's nice, even though it's not quite a perfect fit.) The English word immune has two general uses: (1) biological (immune to disease), and (2) more general ("not affected or influenced by something"), and both of these seem to fit with the computability definition. Immune sets are immune (in the non-technical sense) to the effects of (containing infinite) ce sets, in some sense. 

It also ties well with "productive", as immune sets are somewhat the opposite of productive sets, and in that context, I think of the use of productive as in "productive cough."