The daily login rewards are like an accountwide counter. When you got all, they restart from top left. The catch is, that you have to be careful, from what char you claim. It is like the claim system where in the past you had "accountwide" and "1", so if any char claimed the reward, it was unclaimable for other chars. Same with daily login rewards. You also have to be logged in to that char to claim the reward, you can NOT change the char to claim for on the login screen or rewards window (unlike the old shop system, where you could buy items for other chars while on one different char).
The daily rewards seem to be working better now, if they are worth the trouble once you see the rewards, is up to you

You will get 5 fixed (for now?) challenges you can do each day (basically 3 are easily done while playing). For each tier (contender? expirant? paramount?) there is a different cycle when all progress will be set to zero again. You can see the cycle there by lingering the mouse over the far right box icons. This (or maybe clicking them) will display a cooldown. So basically the first tier resets each day, allowing for you to do up to five challenges a day. These are counted against all three tiers.
Here the catch is, that you have to do them on each char seperately and that you can only do 5 max per day. This makes it important to check the cooldown timers before even starting on a second or third tier. If you focus on one or few chars, you can easily do this though, but you can have a situation (like last week, when they resetted all progress while the system was only 5 days running) mainly late in the month, when starting a second or third tier reward try will be pointless.