Long term storage of Japanese teas should be cold stored, short term, no big deal. Just use them up sooner than later.
Den's does not "nitro flush" their teas, they use de-oxygenators instead. While I prefer the nitro flushing, the deox packets work OK. However I don't think the samplers even have these.
I am thinking the "filters" are simply "fill your own teabags." These can be useful for brewing away from your normal teawares used for brewing, like a restaurant.
For better reponse to your specific questions, may I suggest posting it in the appropriate forum of TeaChat where everyone is more apt to read the discussion.