Nikon D5600 doesn't have image stabilisation. So, I am wondering if I can only use those Nikkor lenses which have VR mentioned? (I am a beginner at DSLR photography and still learning.)
I wanted to buy the AF-S DX NIKKOR 35mm f/1.8G lens but since it doesn't have any VR mentioned, should I not buy it?
There are no Nikon cameras with image stabilization in the body. It's always in the lens, if at all. You don't need to buy VR lenses — although of course if you don't, you won't have image stabilization. This is the case with all Nikon DSLRs, not just the D5600.
I understand where you confusion comes from, because higher-end Nikon bodies have autofocus motors, allowing them to drive (mostly, older or special-purpose) lenses which expect that and don't have their own motors. But for VR, the situation is different.
See Is optical image stabilization a necessary feature for any lens? for some discussion on how vital image stabilization is as a feature overall. The usefulness depend heavily on what you're shooting and how you are doing it. It's also worth noting that while it provides some benefit on a "normal" focal length like 35mm, it's generally more important at longer focal lengths.
