The word θέλω being pronounced as τσέλω is an acoustic error. There probably was some kind of complication with the program, since the voice is not a native speaking, but a Duolingo text-to-speech program. Just like trezost said, Θ is always pronounced like th is in "thanks", no doubt about that. ^.^
I don't think that's possible. The tiles from tile exercises are randomly picked from best translations, and ice cream is in the best translation. It might've showed up in one tile, but cream wouldn't be able to show up as an answer by itself. Are you sure you hadn't use it already, or just didn't notice it was there?
Super interesting observation. I can conceive of this being pronounceable in a way I can't for other vowel sounds at the beginning of words. I imagine that you pronounce the "a" kind of like "uh" and it sort of slurs into the beginning of "ice cream"? That's how it sounds to me when I pronounce it this way, and I think it's because I'm pronouncing the "a" using a sound pretty close in the mouth to where the "long i" sound at the beginning of "ice" starts.
I agree, growing up near the East Coast of the USA, I never heard people ask for "a coffee" or "an ice-cream." They would request "Coffee, please," or "an ice-cream cone." Nonetheless, language is constantly in flux, and I don't doubt there are overworked baristas who talk that way.
This is incorrect. When talking about ice cream sticks, cones, or other individually packaged products, ice cream can be used as a countable noun, similarly to how a coffee can be used, for instance.
So a kid running around in the freezer section in a supermarket can ask their parents for "ice cream" (general) or "an ice cream" (a single product) and both would be entirely correct and plausible.