can I run daemon on xeon phi? And can I communicate with this daemon?
Are you thinking of any daemon in particular? There are a number of daemons that run on the coprocessor already - including the coi_daemon, sshd and nfsiod.
I wanted to run my daemon in native model, but I thought that it will not work, beacuse daemon use external libraries, which I don't compile for MIC architecture. Do I understand correctly?
Yes if the external libraries are compatible with Xeon Phi(TM) coprocessor. But normally you need to recompile those libraries, and transfer them to the coprocessor.