Getting back to original topic: I don't know all answeres, but AFAIK, death shrine works with fighters.
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It is forbidden to kill; therefore all murderers are punished unless they kill in large numbers and to the sound of trumpets. - Voltaire
I can't find the thread where I saw it but:
I belive Units inherit the experiance level of their "carrier". Troops gain from Transports experiance level, ...
I could be wrong.