You have to think this way when you're doing flash, there will be 2 light sources: Available (ambient) light and Flash.

Ambient light is the lights at your surrounding, e.g. let's say you go to a ballroom and the tungsten lights or from the chandelier will be your ambient light. SS and Aperture will affect how much ambient light you can get.

Now for flash it's a bit different. Remember, flash fires very quickly, so shutter speed will not affect much of the flash output due to the fact that the light just flash for a few miliseconds, so there's merely no time for your camera sensor to pick up additional light.

Now why we always get digicam effect (Subject look very bright, but the whole surrounding look like a cave)? This is because the camera, usually at Auto setting will attempt to meter your subject accordingly and at the same time try to make sure there's no camera motion blur due to low SS. So, the camera will think that flash is sufficient enough to lit the subject and hence increase the shutter speed to prevent motion blur. But this will literally kill of the ambient light (slower SS -> more ambient light, faster SS -> lesser ambient light). This explains the cave-like look.

Now to have the foreground and background to lit evenly, we use a technique called dragging the shutter, in which we slow down the SS in Manual mode, i think usually, and what happen is now, the subject is now as lit up as the background. But once again, the caveat of this technique is 1: Low SS will always get you into the risk of camera motion blur, 2: In a typical ballroom or restaurant, if the ambient light is yellow and your flash is white(usually blue), you will have 2 color tones in your photo which usually look undesirable, that is where you have to start playing and adjusting your white balance. Some people uses color gel on the flash. to solve the WB issue. How much ambient light you want to let in to your camera depends on your creativity requirements. Generally speaking, there's no right or wrong.

Your 'cave-like look' is due to when you turn on flash, it syncs to 1/60s slowest on aperture mode. This is usually the default for both digicam and also DSLR unless tweaked. So basically, 1/60s, ISO200 in indoor / ballroom etc. What can you actually expose?