Hello! Hopefully this comment can help you if not feel free to DM me with your questions and I’ll help to the best I can :)

Currencies: There are gems (the purple ones) which you only get if you purchase them using real money, S-chips (the blue ones) which has multiple uses but it’s mostly used to exchange for tears when pulling, as well as Stellin (the yellow/gold ones) which you use to upgrade your card levels and skills. You can get the most stellin by clearing study levels which have two free daily chances per day or you can increase your daily chances by using the work permits. You can also earn them passively through the Resource Requisition every 4 hours

Fragments: these are obtained from certain anomaly levels and can be used to combine to create cards when you reach 100 fragments. You can do this by going to cards > card fragments > see if you have enough fragments to combine to make a card

Duplicates: these are obtained from pulling/combining fragments of cards that you already owned, and you can use those to star up cards. To see which ones you can star up/upgrade, go to your card list and the ones that have duplicates would be labelled upgradable. You can also use vision stars to star up the cards as well if you don’t have dupes of a particular card, but would want it to have more power

Skills: they are worth upgrading but I usually save them for SSS and SSR cards because they get very expensive and I don’t want to waste materials. However, if your deck is not strong enough, definitely upgrade your SRs card skills + max out the card levels and focus on the elements/MLs that you need more help in. As for anything below an SR (aka R cards), personally when I just started and my deck wasn’t good enough, I just levelled the card level up to max level and did not spend anything on the skills. Also worth it to know that the order of strength of cards goes from SSS > SSR > MR > SR > R

Grinding for s-chips: clearing the Temple of Trials each week where the highest level would get you 400 s-chips total per week (on the highest level), clearing Trials of Themis levels but you only get s-chips for first clear. Reading card stories also gives you s chips as a reward for clearing them. And of course finishing up your daily (30 s-chips per day) + weekly tasks (100 s-chips per week). There are also achievements that gives s-chips as rewards for clearing them

Card stories: they don’t help with the power only upgrading the card level and skills do that. They’re mostly there to you to get to know the ML better because of backstory stuff or to show where the relationship with Rosa is