Should I consider 35mm or instead buy a 55-200mm for better range?
Yes. Prime lenses usually offer both superior image quality and larger apertures compared to zoom lenses of similar price. This is due to simpler mechanical construction, as less moving parts are needed, and due to especially chromatic aberration being easier to correct for just one focal length.
The decision between 35mm and 55-200mm is in the end about your needs - 35mm lens gets you close to the 50mm-on-full-frame that has often been considered as the "neutral" focal length, and the one to use if you need to pick just one. Also, fast prime gives you ability to shoot concerts and other performances, and different kinds of indoor events in general.
55-200mm gives you more reach, and can be useful if you want to capture small details outdoors, or get perspective flattened up.
The answer to the question "should you consider a 35mm lens" is obviously going to depend a lot on you and on the type of photography you like to do. However, there are at least two factors (other than the very different focal lengths) that set the 35mm f/1.8 lens apart from the other two lenses.
1) Speed of the lens (how much light it lets in):
An f/1.8 aperture will let in around 4 times the amount of light as your 18-55mm. The difference this can make in indoor shooting is huge. A further consideration is the depth of field advantage that an f/1.8 lens will give you; you will be able to blur the background to a a much greater extent than with your current lens that covers that focal length.
2) Image Quality:
As a general rule, the faster a lens is, the higher the quality (and price). There are certainly exceptions to this 'rule', but it is usually the case that for a given aperture setting, the faster lens will be sharper. For example, shooting at f/4 with your 18-55mm (set to 35mm) and at f/4 with the Nikon 35mm, the 35mm will produce a better image.
* It is also a general guideline that prime lenses (fixed focal length) will have better image qiality than zoom lenses, due to the nature of the design of the optical elements.
Using prime lenses indirectly make you think a lot more about composition. This is fantastic to learn and find a style, yet comes with challenges. My favorite setup is a 50mm f1.4 and a 5D (which would have a comparable FOV to the 35mm on the D5100)
Using only primes for event photography. I will never forget one of my first paid events.
I tend to have a facebook oriented distribution, and from a meeting with the clients, all I really had been hired to do was get people new profile pictures! Profiles and half body crops were all I was aiming to shoot.
All I took to the event was a 50mm on the old 5D mark i and a flash. When the guests started arriving one girl was adement that I should get a full portrait of her and her friend. I took a few paces back and with my back against the wall and I still couldn't fit them both in. We had to march through to a larger space in poor lighting and try again there.
Using a prime means you have to move around to get the composition how you want it. This is rarely convenient. Even taking several primes is a faff. My new setup at events involves two cameras, one with a standard prime, the other with a zoom.
Street photography. Although stressful in a professional context, going and doing street photography without a zoom function is very liberating. You have to often get yourself right in the heart of the scene to get the shot (unless you're using some 500m Tamron jobby!).
Numbers aren't everything. Consider both lenses before you spend wads of cash. I think you should try out the lenses for a couple of days and then buy which ever you prefer using. No other answers cover this aspect of fixed length lenses. The internet is already bloated with people praising the prime lenses for the optic quality and faster apertures.
I run a photographic society and we have a community thats friendly enough to share lenses. A member recently purchased a Canon with the kit lens and a 60-200mm zoom lens. Dissatisfied with his choice, I lent him the canon plastastic 50mm and within a few days he sold the zoom tele photo lens and bought a 50mm prime. All the members who have tried primes, go out and buy them. They do tend to just stay attached to your camera.
I use my DX 35mm f1/8G in almost all situations, I zoom using my feet. It's great especially in low light scenarios. I love its bokeh especially in f/2.8.
About the 18-55mm, other people swap it with 35mm, but I suggests not to or totally abandon it after getting that portrait lens. It is very usable in almost all (mid-to-high light) situations, from semi wide angle to semi telephoto. Take in mind that in DX cameras, focal range below 35mm is considered as wide lens. Lenses that go below 18mm are very pricey. If you're not a photographer working on the industry or in the field, I don't think you would need that pricey wide angle lens and therefore the 18-55mm can give you the wide angle.
I have a Nikon D3000 with 18-55mm and 35mm lenses. To date, I have obtained better images from the 35mm lens, both indoor and outdoors. According to you which one is better.