On the January 5th sheet it has two instances where it say a student is perform a skill & one where the Arcane Adept is performing one.  Are they both the same?  Or is the student new & if so, what are his/her stats?

It's not a person, it's an ability reminder, although for an ability that neither of our possible characters has. For the 1st roll, both Severin's 'Arcane Adept' and 'Arcane Knowledge' skills could be used I think. For the 3rd roll, as it's charisma, just the 'Arcane Adept' makes sense to me.

Came here for the same issue. I saw "Student" is an ability that comes up later after leveling up. Seems like a mistake to add it as a reminder at this point.

We originally had Severin with the Student ability but had to rework the character in testing. We forgot to change the calendar in accordance.