1) As far as I'm aware, you don't have to claim rewards or even watch the streams.
2) My account is a year older than yours, and I'm currently sitting on 1.9k crafted forma and 687 potatoes. Resources? When am I ever going to get through 1.8k nitain? Inventory slots? I don't recall having had to buy inventory slots in a long, long time other than for companions, but have a dozen spare 'frame slots from NW and event rewards, and can free up to a total of just over 70 weapon slots if I sell 50-odd weapons that I never bothered to invest in once maxed; if I needed more I can get more plat if I could ever be bothered to trade any of the easily 200k+ ducats worth of mostly vaulted prime parts that I've accumulated. Even with a year less playtime, if after seven years you still need "something useful for gameplay" then I respectfully suggest your horizons are very, very limited.