There’re two things mixed in your question. @InkiteeWorkshop has explained perfectly the part of the daily check in event, but there’s the other part:
Not exactly, the mini store is the Mini Awards Store topic itself. If you revisit it, you’ll see it says you can redeem at the end of the month by DMing Elena 
for that, you need enough cheer points to get the redeemed product, but you may not know how many you need if you want something that is not currently displayed on the store table image. But the store is a concept, it is not a place you can access, when you reach a given amount of points, or anything like that.
If you want to target a rough amount of cheer points necessary to a particular product to redeem, you can follow the ROUGH rule than 1000 cheer points equals AROUND 10$ of the real product official prize. Let’s say, for instance, that a Mini Press costs AROUND 6K cheers. But please, I’m not an admin, I just want to help you having a notion to help you decide and plan what are you saving for, and this rule is a conclusion I get by observing different conversions, and the rule doesn’t seem an exact equation. That conversion rule I made up is orientative.
So make your plan and when you think you have enough cheers to redeem your desired product, contact Elena and ask her about the exact amount and availability in your location. But you can also DM admins whenever you need, you don’t need to wait. They always answer very kindly, they are very cool girls