Hey Nicole,
Welcome to the forum! I can understand why you don't like to use flash. Actually, most people don't like to use it if they don't have to. Flash photography is commonly misunderstood. The reason why so many people hate flash photography is because, well, they simply don't want their photos to reflect the fact that they used a flash. If used improperly, you'll almost always get this artificial look. However, if used properly, your flash can provide you with balanced lighting every time.
The reason why your backgrounds are so dark and your subject is so bright is because, well, first of all, you're shooting indoors and there's not much light available to you—that’s a given. However, we can combat this. Start by opening up your aperture to let in that beautiful ambient light that we all know and love. Next, decrease the shutter speed by a few steps—say 1/30 or so. Now, I know what you're thinking: "Well, now my subject is going to be blurred by camera shake." Relax, sister; Pentax's Shake Reduction has got your back. Even if you don’t have advanced functions like Shake Reduction, your subject is effectively frozen by the burst of light provided by your flash.
Now you want to take it a step further. You don't want that fake "deer-in-the-headlights" look. Pick up a flash diffuser. This creates nice, soft, natural-looking light, and lights up the whole room. Bounce flash is better than direct flash, but it's still not great. For example, not every building has a low, white ceiling. Even so, bounce flash makes the subject's eyes appear sunken, since the light is now coming from the ceiling. I would suggest the Gary Fong Lightsphere II. Since you're taking mostly portraits and are up close to your subject, I'd suggest the Cloud version. The Lightspheres are pricey for a piece of plastic that probably costs cents to make, but they're worth every penny. It's currently the best flash dispersion system out there, except for the Whaletale, which is also a product by Gary Fong. Follow these directions and you can produce some stunning photos with nice, balanced light.
As for lenses, if you're taking a lot of indoor portraits, I would suggest a faster lens. What do I mean by “fast”? Well, a lens' speed is determined by its maximum aperture—how wide it can open to expose light. Lenses with f/2.8 or below are generally considered fast, while lenses f/2.8 and above are considered to be on the slow side. That doesn't make it a bad lens, it just can't let in as much light as a faster lens, and thus can't use faster shutter speeds to freeze the subject. Slower lenses are generally used for more ideal lighting conditions.
As for a specific lens, the FA 50mm f/1.4 is a good suggestion, because it's relatively cheap and fast as hell. However, if you've got the money, I'd look at the Pentax's Limited prime lenses. If this is what you want to do, look for something in the 70mm-100mm range. These are generally referred to as portrait lenses, since they provide a more flattering perspective for your subject; wide-angle lenses generally distort your subjects facial features, ultimately making them unhappy campers. However, sometimes that's the look that photographers go for. But, I agree with what some of the other people in the forum have said: play around with your zoom lens and try to find your sweet spot—your most frequently used focal length. Then, base your decision off of that when you're looking for a fast prime lens. I hope that helps. Let me know if you have any more questions, and I'd be glad to help.