Softkeyz is a root app. Yureka runs CyanogenMod out of the box but I don't know if it's rooted or not. Is it safe to install softkeyz root app and use it?
CyanogenMod comes with root support, however it needs to be enabled first from the settings app in the developer options section.
Also, CyanogenMod cones with the ability to modify the navigation bar already, unless you are talking about modifying the actions of physical navigation buttons, then you'll need the Softkeyz app.
First of all, there is a glaring error in the question which needs to be removed. Yu Yureka doesn't come with Cyanogenmod (CM; a community ROM) but with Cyanogen OS (COS12) which is a stripped out CM12 ROM meant to suit the needs of an OEM (a commercial software). Read this XDA thread for more.
As one would expect, COS12 doesn't come with
su binary or a superuser app. In simpler terms, NO, your device isn't rooted yet. You can verify this with any root checker app and they should give you negative result.
Is it safe to install softkeyz root app and use it?
The app has full network access (read: can connect to Internet and send or receive data) and has access to your storage (ability to read or modify your data). Besides, it needs superusers access as well.
If the app isn't open source and and its source independently verified by people, I say your part of question is speculative since there is not much can be said with surety.
Coming to the point of this app's usage, if your need is to get the navigational bar then why bother installing a third-party app. Cyanogen OS comes with in-built navigational bar (yes, those virtual buttons at the bottom of screen). Simply go to Settings -> Buttons -> Enable on-screen navigational bar. Done. You can somewhat modify the buttons as the other answer by Sonickyle27 noted.
adb shell settings put secure dev_force_show_navbar 1
This would enable on-screen navigational bar. Change 1 to 0 to disable it.