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You are correct.  The gift list is randomly generated when you create a game.  Once you upgrade certain buildings to certain levels, some gifts disappear, and you get new gifts.

Your warehouse contains the things you acquire through flights, gifts, space launches and collections from neighbor visits.  You can not gift things from your warehouse.

As far as what you need, and notifying your neighbors, if they are forum members, you can PM them, or simply post in the Weekly Windows Trading thread and request those items, and also place them in your signature for others to read.  Non forum members is hit and miss, unless they lurk here.

Hope this helps and happy flying!