No. Objective Lua has no relation to Objective C other than borrowing the syntax and part of the name. The Objective Lua class hierarchy is entirely different (although it's inspired by it). The distribution package is completely standalone and requires no additional software other than Lua, Lpeg, and (optionally) Lua Markdown.
Right now, no, but I'm hoping to see one soon.
None. It's all in pure Lua.
Objective Lua code should run at the same speed as classic Lua code --- that's what it compiles to, after all. Objective Lua method calls are identical to Lua method calls.
However, right now creating Objective Lua objects is quite expensive, so if your program does a lot of object churn, you may see performance issues there. Also, the natural Objective Lua coding style is to use lots of little methods rather than a few big ones, so there is increased overhead due to more table lookups. Of course, you don't have to write your code like that...
Naturally. It's much faster, too.
As it's all in stock Lua and contains no platform-specific code, almost certainly. I only tested it on Linux, though.
That's a very good question. And the answer is... I don't know. If anyone gets it working, please let me know!