I have just bought my first DSLR, a Nikon D3300 with an 18-55mm lens. I want to enhance my reach and purchase a higher lens. My choice is a Nikkor 70-300mm but one of my friends said that as my camera is currently working at 55mm, I have to go for 55-200mm or 55-300mm lense only. Is it true? Can I not use 70-300mm lenses on my D3300? My major purpose is to shoot landscape images.
Your friend is wrong. You don't have to get a 55-something telephoto zoom, unless you don't want a gap in focal length coverage. A lot of us would say that the 55-75mm range probably doesn't matter, while the additional length of a 300mm lens over 200mm lens is probably worth it. If you do care about range coverage without a gap, then getting an 18-300 supertelephoto might be a better alternative, but with more image quality compromises at the ends of the range.
You can use FX lenses on a DX body with no issues. And, as long as it's got AF-S, it will autofocus on a D3x00 entry-level body.
However. You do need to be aware that using a telephoto zoom lens can be more difficult than using a simple 18-55 walkaround. Most reasonable-cost 70-300ish telephoto lenses tend to be slow (i.e., have a maximum aperture in the f/4.5-5.6 range) to keep their size small and the cost low; and like any lenses, will typically perform better stopped down from wide open (i.e., f/8-f/11). 300mm is a lot of a reach, and a lot of magnification which will effectively increase blur from camera shake while handholding. Know the 1/focal_length rule (i.e., that you want to use at least 1/300s shutter speed for a 300mm lens; or 1/450s if you count the "crop factor" of a DX camera). Know good long lens techniques, and consider support gear if you need slower shutter speeds.
The right answer for your friend or for me may not be the right answer for you.
For me, the number of possible shots I will miss between 50mm and 70mm is many fewer than the number I will miss between 200mm and 300mm. In part because it is more likely I can 'zoom out with my feet' (walk away from the subject) to cover a gap at shorter focal lengths than it is to 'zoom in with my feet' (walk toward the subject) at longer focal lengths because the distance is greater at longer focal lengths and because I often use a longer zoom when it is impractical to get closer to the subject. For example to avoid startling wildlife or interfering with a sporting event.
Finally, it is possible to create great photos with only prime (fixed focal length non-zooming) lenses or even a single fixed length lens. It's all tradeoffs.