hii ! you need to increase your talent to score s ranks, you should be able to hit it around 180 - 220k. yes you should level a team of same group + type/attribute.
you also need to level up the area items around your sekais and the plants in each school - this is why it's good to do same group and same attri, because you'll get a bonus if every card in the team is the same attribute.
if you s rank a song, it's s ranked on all difficulties. so you don't need to fc every song on easy and medium if you don't want to! they only give coins, but you may want to do them in future if you find yourself running low on coins xD (you will run out, area items are so expensive)
because only hard/expert/master gives crystals personally those are the only ones i play if i'm not grinding coins
another note is the large talent range is because your score will vary from song to song. shorter songs give more score (this is why it's meta to play short songs like hitorinbo envy, bless your breath and cendrillon for your challenge live!). so if you want to hit s rank earlier, try shorter songs
lastlyy sorry i'm such a yapper but there's no need to force yourself to do anything "for progression" in this game. there's no competition outside of tiering and ranked match so like, just play what you think is fun~ after you can consistently get s ranks that's all you really need for maximum crystals