I might be wrong, but I think math favors different starting indices based on the subject matter. I've seen Analysis textbooks favor 0 as the starting index. I don't think there's a clear argument for cultural transference from math.
I'm opposed to starting index from 1 because I think departure from very mainstream programming tradition should have a strong reason beyond preference, even if the de facto tradition appears equally capricious.
Debatable. It makes sense to say "the first element", regardless of mathematical connotations. We've had this kind of expression in almost every language across the world long before we invented multiplication.
Saying the "the zeroth element" is just... weird and slightly nonsensical.
I agree that is very weird at first. But after building a toy project including about 5,000 lines of Lua, I can say I got used to it fairly quickly. Most of the time, I was accessing arrays via iterators anyway, so I had to deal with indices very rarely.
Aesthetically, it is repulsive, but when actually writing code in Lua, it was not much of a problem. I felt much stronger about "do"/"then" and "end" versus curly braces for delimiting blocks.