I have been playing this wave matching mini game as I explore and I gather these resources that are minerals and particles and technology and I don't know what it is for. It doesn't have any sell value but before I discard it, will it sell on the exchange? Is it worth anything to anyone?
The answer to your question is yes on both accounts, let me explain.
All minerals, particles and technology can later be used to create items yourself at Memory Alpha or DS-9. I think they are the only two places in Fed space. However crafting your own items requires lots of all of them plus you need to either craft or buy the appropriate schematic first. Then it takes even more time to build up your experience at fabricating items in order to make even better ones that are worth using. On the flip side, you can fabricate items and just go and sell them on the market.
As far as selling yes you can sell them on the market. Best bet is to go to the market, run a search and see what the average price is. The Rare resources can fetch a decent price out there.
In addition to crafting, data modes cam be used on teh Duty Officer system and Fleet System Teh Dutty Officer is a new system you'll be introduced to when you are level 11. The Fleet System is how you build you Starbase for your fleet if/when you ever joing a fleet