If you're on the JVM, and if you're compiling J down to JVM bytecode (much as April compiles APL -> CL -> machine code), and if your data is stored in primitive Java arrays, then you'd get pretty close to C speeds. Or at least J speeds (where J is implemented in C).
That's a lot of conditions, but it's not completely crazy. :)
Maybe. Java is quite fast, but for very different reasons than APL; I don't think it would transfer that easily. Part of the reason APLs are so fast is because the interpreter and all the code fit in cache; my copy of k is 76kb. I don't think there's a chance you could get that with the jvm. APL also relies heavily on SIMD, and I don't know how well-supported that is on the JVM.
Unlikely; clojure runs on the jvm (or on top of js), and interop with c is slow.