"When we click on the page with previously released singles, I would like a little button displaying who the center of that single was. "
With the latest update, just hover your mouse over the song to see the center.
"When getting girls into contracts (TV shows/advertisements) it'd be super useful to display how many contracts they're already in and how much stamina they're losing per week."
Right click on the girl's portrait to see this information.
Ah sorry, I didn't notice the ability to hover over the past singles in the new update. Even so, I think it'd be nice to display a little logo of the face of whoever was the center. I don't really have my idols names memorized but I know their face and hairstyle haha. I can then keep in my head "blondie and bob cut were the last 2 centers so I won't put them this time."
As far as contracts, I mean when the contract window pops up with the 3 idols to choose from. It'd be nice if alongside the new stamina logos, there was perhaps a minus sign, showing minus how much stamina they are losing to contracts per week or something like that. I usually have 15 idols once I have enough money and that's too many contracts for me to keep track of without it being displayed. So it sucks when I accidentally give an idol 4 contracts because she has high stats but then I have to cancel 1 or 2 so she's not losing like 60 stamina a week.