MacBook Pro going to sleep by itself because of watchdog daemon
Here is the readout from your logs.

Your BTLE (Bluetooth low energy) is shutting down (normal ?)

The watchdogd is shutting down the corresponding processes, but is is not meant to shut down your system.

The SystemWillSleep is for the coreaudiod, due to the airplay shutting down, it does not mean the OS X shutting down.

All of the above is happening because the OS X received the sleep command (they happen after the command was issued).

The OS X will sleep if you have something like kernel[0]: sleep

and more info can be found 

kernel[0]: Previous Sleep Cause: 5


New logs show:

Your system did enter the sleep mode.

It was woken up by the RTC Alarm. Check your Energy Saver settings-

It was woken up by the WOMP since it is enabled (Wake On Magic Packet) a network.

To see all wake up reasons use syslog |grep -i "Wake reason" in your Terminal.

So far your system is not acting strange, just doing what you asked it to do. The "restarts" you are referring to are the wakes ups from sleep mode. There is no log entry showing that the system has restarted.

If it did the restart then you would see for example:

shutdown[15811]: SHUTDOWN_TIME: 1424885403 656386

bootlog[0]: BOOT_TIME 1424885410 0