Both Kurama and D's class entries are up-to-date. This covers the Mythology, Botany and English Horseback Riding classes. Kurama's Botany class hasn't officially begun yet, but he'll be announcing to the dome this month, with the first session being held on whatever the next in-game day ending in the correct number is. Likewise, D hasn't announced that the riding lesson idea is official, but will be doing so this month.
So, basically, no changes needed to those three classes unless I've messed up with the scheduling and need to adjust the location and/or times to honor prior claims!