First questions - probably with autofilter. Especially if the layout is vertical. After showing only "non-teaching" days you can mark all visible rows with dates and delete them (if dates are a result of formula do copy-pastespecial as values before filtering).
As for grading usefull functions could be COUNTIF or COUNTIFS and probably sooner or later you will use also VLOOKUP.

Not seeing attachement it is probably end of suggestions.