1. Better spend B coins on low tiers or on high tiers?
This would depend on #3. You would want to maximize coins. If the XP resets, you do it lower. If the XP doesn't reset, you do it later.
2. Bought tier skips, counts for Badge progressions?
I don't think so, badge says "earned"
3. Does the XP resets weekly?
Great question. Resetting would seem to make people play less. You would get a bunch of people only playing up to a certain point, then waiting for the reset. If it doesn't reset, it is sort of an even playing field, regardless of when you gain XP. So I think it won't reset, but could be wrong. Also, if it resets, players will hit 100 a lot quicker AND then stop playing.
4. Tier skips = rises tier XP requirements?
I don't think it would as the Tier Skips are not technically XP based correct?