How to update Galaxy S4 GT-I9505 from Lollipop to Nougat Android 7.0 version? How to update the Galaxy S4 GT-I9505 from Android 5.0 Lollipop to Android 7.0 Nougat (without Root)? Currently not getting or not showing any updates either with Software Update or from Samsung Smart Switch/Samsung Kies in Galaxy S4 device.

Additionally, I do not see Android 7.0 Nougat version updates in SamMobile website with respective to the firmware.
It's simply not available, and likely will not be due to S4's age (3+ years - most manufacturers won't support beyond 2). See how it doesn't even get Marshmallow yet?

There is much 3rd-party development for the device, however, and an AOSP-based Nougat ROM is available. You do need to dive into the world of flashing custom ROMs (*) which could take some time, there will be bugs in the beginning, and you will lose many Samsung-specific features should you decide to do the switch, but it's the only way out if you want to stay on the cutting edge.

*: On Samsung devices, flashing a custom ROM usually doesn't require root, but custom ROMs often come with root.