Yes, the "Crimson Days" card in Activities->Other Activities is awarded when you get to the Tower, or maybe after talking to Lord Shaxx and accepting the quest, and does not carry Grimoire Points. Yes, Crimson Doubles wins have counted for me as Doubles wins on the Doubles Grimoire card. Prior to my first Crimson Doubles match, it is worth noting that I had finished accruing at least 100 wins to my Elimination card, which might have affected this. Moreover, the wins that are counting for me are match wins, not round wins. Furthermore, it is only awarding 1 Crimson Doubles win per match win, not 3 wins per match completion the way Elimination tends to count wins for me.