I volunteer as an ESL tutor several mornings a week and noticed several of my adult students from different countries using Swahili as a common form of communication. I decided it was time I attempted to meet them partway! I love the patterns and rhythm of the language, and even more important than the vocabulary acquisition, it has been good to be reminded of what it's like to learn something new.
I agree, though our university has a dept of African languages and the professor says they can argue about that question for hours.
One school of thought says "Kiswahili" is the actual name of the language, so you should use that; others argue that, in the context of a conversation in English, the language is called "Swahili" (just as the German language is called "Deutsch" in German, "allemand" in French, "tedesco" in Italian, and "tyska" in Swedish).