If you lose the symbols you lose the terse nature of the language, which as far as I can tell seems to be one of the most alluring parts of the language (the author of the blog post shows game of life as essentially a one-liner).
Did you read any J programs? It is just as terse as APL. (Probably K is pretty terse too, but I won't comment on it as I only know J.)
In J, the parens, brackets and braces aren't balanced because those 6 symbols, i.e. `(`, `)`, `[`, `]`, `{` and `}`, are used as standalone symbols for other syntactic stuff, making J code very hard to read.
Parenthesis are paired and have their usual function of groupoing. You are correct about brackets and braces though. Personally I do think J is often hard to read, but not because of the unbalanced brackets and braces.
No, parens are parens, used for grouping. The rest is true, though: brackets `[`, `]` are essentially two flavors of identity function (dyadic) and `{`, `}` are indexing operators (not sure I remember right, but I think `(<1;2) { A` would be `A[1][2]` in more common languages).
J and K are extremely terse, though. They just chose other ASCII symbols that exist on everyone's keyboard.