What advantages will a 35mm lens will give me if I already owe an 18-55mm. Isn't the 35mm somewhat included in the other one? It may be a silly question, but I am new in photography and trying to understand the lenses.
Yes, the 18-55mm lens will of course also do 35mm. This focal length determines the angular field of view of the lens. So the 18-55 is more versatile in that way. Because 18mm is a 2x wider view (than 35mm), which is called wide angle, and 55mm approaches a magnified or zoomed in view, of about a half again larger subject (in a smaller zoomed view than the 35mm, a mild telephoto effect). You can see this effect by zooming your current lens and looking. The 35mm lens only does 35mm. It is however the approximate "normal lens" or normal focal length for the DX sensor - meaning a good choice of view in many average situations. But your zoom lens can also easily choose 35mm.
The aperture of the f/1.8 lens (if used opened to f/1.8) can see 2 stops (4x) more light than the f/3.5 lens. A brighter view in a darker situation, which allows lower ISO or faster shutter speed. However, which is also less depth of field (smaller zone of clear focus, sometimes intentionally done). This however is a very special situation. Routine photography is better (sharper) in any lens used up around f/5.6 or f/8.
These are the very first basics of choosing lenses.