Can Perl be used to create a message broker applications,

Yes, you can make anykind of socket connections you desire. See IO::Socket::SSL GTk2 server and multiple clients for example

a FTP file transfer application
Yes, see commandline ftpssl client with Perl which was quickly written in Perl, when there
was no available working ftpssl client, which wasn't a binary. Perl
did the job.

You should check out what modules are available to you in whatever language you choose. Perl does not do as good of a job with the graphical user interface stuff, or Android development. Perl5 has some excellent but less-known Web interfaces

What I suggest is prototype your system quickly using Perl, then convert it to whatever you want.