A few questions regarding on the Tower event, items, etc

I apologize if these answers seem short. I feel a little rushed. Next time, go to the general discussion.

The new wave guide is a little outdated because the game mechanics do change a little bit about every 2-3 months I would say.

1) That gem was for rebirthing the LR Tsubaki.

2) Match the symbol with the red and the white.

3) Yes rebirth means combine the same cards. Asuka doing chemistry changes when you combine the same amount of times.
However, you do not have to reroll her 5 times, just need the UR GK card (it's the yellow/gold card for UR, silver for SR, and purple for LR)
Those cards make it easier to rebirth.

4) You raise team rank essentially by playing the game and leveling up.

5) If you do the gacha slayers, it takes you to a menu. However they cost money and chances are you probably have zero unless u used money.

6) Not exactly. You get a free roll of a separate gacha if you have the tickets from the last week of the month. It's in the second tab. You just have to make sure you log in every day of the last month and sign in.

Hope that helps! If not ask questions here or in the general discussion (which is typically more active)