yes, Alum is both a specific chemical compound and a class of chemical compounds. The specific compound is the hrdreted potassium aluminiumsulfate (potassium alun) with the formula KAL(SO4)2.12H2O). The wider class of compounds known as alums have the related empirical formula,AB(SO4)2.12H2O.
Aluminum sulfite is neither an acid or base, it's a salt. However, when combined with water or another substance, the entire solution can become either become an acid or a base depending on the direction of equilibrium (kPa).
Here are some examples of bases and their respective formulas:
Calcium Hydroxide - Ca(OH)2
Sodium Hydroxide - NaOH
Potassium Hydroxide - KOH
Barium Hydroxide - Ba(OH)2
Notice how all of these bases have an Hydroxide Ion (OH-), this is often a general indicator that a substance is a base. However, this heuristic should only be used for common substances and is not true for all compounds containing OH (especially complex substances).