About " kusafisha" and "kuosha" - in my language the difference is evident. You can " kusafisha" the bathroom cleaning floor, bathtube walls.... And also another parts of hause, but you can't " kuosha" this. You wash the dishes, pots etc. and it is called " kuosha". Sweeping ( kufagia ) it is still another kind of cleaning. I hope that my explanation helps a bit.
"Heavily influenced" is an exaggeration. The influence is superficial, some greetings and the occasional word loan like in many other widely spoken languages (French and Spanish for example) because Arabs interacted with the local people or native speakers. You're right about the name of the language, it specifically comes from the name Arab traders called the people living off the Indian ocean coast, whom they encountered first before they got inland in modern day east Africa.
The bulk of Kiswahili, i.e. the grammar, noun classes, etc. is very much like that of other Bantu languages, Congo-Niger languages specifically. Other African languages are closer to Arabic, like Somali, and it's easy to tell because they belong to the same large Afro-Asiatic language family.