@@Cole11111-f S+ is the best rank overall for BT and after that I would ask you to go for his Exclusive weapon. And yes the buff was to the baseline Blazing Tempest and not other ranks.
Well, Bloody Palace once every reset for 360 gems per week. Do the dailies for 60 gems. Boss hunt for 500 gems and any new events that may or may not arrive. Realm Conquerer can be done too but that a one time thing. Then we have a free road on Coop mode that gets reset every week or so and PVP Road as well which arrives sometimes if you're interested in that of course.
I noticed your comment too late and maybe you've figured things out on your own. Well, I'd say have at least one card with Burn Guage Efficiency. Go with ATK or Crit rate or damage on the third card depending on what's lacking. Make sure to balance out crit rate and Crit damage on 1:2. You can have HP on the last card but I did share my BT cards on the post if that helps.