Well, a R&D center should be able to find answers to most of these questions itself, wouldn't it? As for the questions:
If I were to say "very succesfully", would that statement mean anything to you? Perhaps my "very" means "hardly" to you.
Yes there are. But if you mean "are there any compilers that can turn a non-trivial piece of Perl code into compilable and runable C code", then the answer is no. Unless you mean a compiler that just spits out a piece of code that has an embedded Perl compiler and the code you want to run wrapped together. A lot of work was done on perlcc. However, that work was done in the 5.004 era. No significant development has been done on it since.
Yes. But then, so can a piece of Java code used to print bar codes.
No. Not even perl itself depends solely on perl. Perl depends on C (it was written in C, has extentions written in XS/C, uses dynamic libraries written in C). It also needs on OS to run. It needs hardware to run on. And that hardware needs power to run. Companies also depend on their local mail provider, delivering mail every day. They depend on banks. On janitors. And on their employees.
No, it's not true for Perl. Perl does have limits, although some are set by its environment. But there are theoretical limits as well. Perl is equivalent to a Turing Machine - anything that can't be calculated by a Turing Machine, you can't calculate with Perl.