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Haven't read any of the rules for this (or for that matter the last couple 40k editions) but I've got some friends who might be getting into it. Wondering firstly if it would be possible to run a team that had one each of the different Eldar Aspect Warriors, and secondly would that even be any good?

The only aspect in SWA is Dire Avengers.
House-rule it, but that's all you get.
The rules for CWE are downloadable: https://www.games-workshop.com/resources/PDF/ShadowWar/SWA_Killteams_ENG.pdf

If you go over to the Yaktribe.org website and check their forums someone has put together a homebrew Aspect Warriors list. No idea how balanced it is but it might be a starting point.