Lets Do Some Math

I currently have 280 BE but for the sake of this post we'll pretend i have 0 BE. A rune page cost 6300 BE and the average BE worth of a capsule is 910. Additionally, every 10th capsule is worth 2120 on average. You earn on average 250 XP for a 30 minute win and 200 for a 30 minute loss with your first win of the day being worth 500 XP. So the numbers i don't know are:

1. How many games would it take per day to gain one level?
2. How many would it take it two days?
3. How many levels would it take to earn enough BE for a Rune Page?
4. How many would it take for a new champ at full price?
5. Is Riot correct when they say this system will give you champs faster than the old one?