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[Eagle of Fire]

It is probably possible to rush the flying suit research but it would be at the cost of everything else. It is not really wise to do that especially since the flying suit give marginal armor upgrade over the second armor. Only the flying is handy.

For the Chrysalids, as I already mentioned, your soldier become a zombie if he gets killed. I had soldiers resist 3-4 Chrysalid attacks in the same round before so it is definitely not an insta-kill attack.