I think Julia is the largest application of itself at the moment - the majority of functionality is written in the language itself. The time-to-repl is 2-4s depending on your os and setup. Taking package loading time in to account, it can be an issue, but there is a plan (and code) to address this soon.
Yes. There is a patch which provides static compilation support for the system image and should eliminate the startup time. However, the changes from 0.1 have been enormous already, so this will not be merged until 0.2 is tagged.
it's a JIT, so it's progressive compilation in some sense. BUT i certainly noticed that it seemed slower than python when starting a program. not java slow, but not instant.
I'm a little concerned because it seems to be doing a fully optimizing recompile on every invocation.