Now for the 3rd person sg, do we never use the prefix "a" if it is not a human?
It depends on the noun class. So for "kiti" (chair), which is in the ki/vi noun class, you'd use "ki". ("The chair was nice" would be "Kiti kilikuwa nzuri.") For "Nyumba", which is in the n/n noun class, singular subject prefix is "i", so for "The house is nice", you would say "nyumba ilikuwa nzuri."