I'm not 100% sure since this event is new for me too but on your questions:
The game gives a countdown timer at the colloseum. This should be it (The same time when you get a new daily inlog bonus). Be careful if you want to play at the end of the day though as there is a five minute cooldown between each battle. I hope you don't live in a bad timezone.
On the claiming thing. It doesn't matter anymore. Try to claim every 24 hours though or else you'll lose out.
It's so much faster on Android, and you'll want that speed when trying to reroll fresh. Took me two days of rerolling to get my Nympha to start. That was prior to v2, so at least you have that going for you.
Use the free version of Genymotion for android device emulation.
Once you have a device set up, to reroll all you have to do is:
1) Navigate to Android settings
2) Go to the Apps menu
3) Locate Chain Chronicle and tap it
4) You'll see a bunch of usage numbers and data. There should be a Clear Data button. Hit the button, and you're reset.
Yep, this app here for android. Though admittedly the second image there I made even more ridiculous by adding extra red filters :D