There are 3 anions in Al2(CO3)3 because there are 2Al 3+ ions, and 3 CO3 2- ions. The 2- ions are the anions, because they are negatively charged, hence there are 3 in Al2(CO3)3.
Dissociation is exclusively an ionic trait. NaCl is a good example. NaCl(s) will convert into Na+(aq) and Cl-(aq) in water, which is a dissociation process. If you are talking about solubility, however, polar molecules (covalent) can dissolve like salt, but it is not dissociation, it is because of dipolar molecules, rather than charged ions.
Ionisation is the formation of ions, and a good example is the addition of two volatile elements. Na(s) and Cl2(g) will strongly react with each other to form NaCl. The solid sodium metal give an electron to a chlorine in the chlorine gas molecule and two ions are formed, a positively charged Na+ ion, and a negatively charged Cl- ion.
Don't know about water treatment, sorry.