"na" at the beginning is because "napisati" is perfective verb and "pisati" is imperfective verb ("na" is in this case, typical prefixes to create perfective verbs are: do, iz, z, s, se, na, nad, o ,ob, od, po, pre, pred, pri pro, raz, u, v ,vz, za ... - and there is no simple rule when to use one and it also depends on meaning).
No, for a girl the ending is -la:
Napisala bom pismo.
or
Pisala bom pismo. (I'll be writting a letter.)