Of the three factors -- character level, Cryptarch level, engram level (rarity) -- what actually matters more in determining the quality of a decoded item?

I don't think anything influences quality of what's actually decoded. All I've noticed is that your level seems to cap the minimum level items are decoded at.

Does the Cryptarch level not influence the quality of the item directly but only the rarity of the engrams he has for sale?

I'm not sure on this, but I think it's just what he sells. I'm almost rank 5, and haven't really noticed any change here.

Does the quality of items scale with your character level or is it independent? (I've seen it recommended by some to hold all of your engrams -- even whites and greens -- until you reach level 20...)

Quality itself doesn't seem to, just the level. I'm level 24, and I think the lowest I get now is 18. So I guess holding makes sense, but really I'd say only Legendary or Exotic would be worth it. I get a ton of Rare now. Even then, my only Legendary engram so far was 2 Motes of Light.

Of the three factors -- character level, Cryptarch level, engram level (rarity) -- what actually matters more in determining the quality of a decoded item?

Does the Cryptarch level not influence the quality of the item directly but only the rarity of the engrams he has for sale?

Does the quality of items scale with your character level or is it independent? (I've seen it recommended by some to hold all of your engrams -- even whites and greens -- until you reach level 20...)

Any insights would be helpful. Thanks.

-nash