I have a Nikon D5100 with the excellent 35mm 1.8 (DX) prime lens and am now looking at the 50mm 1.4 (FX). This is (according to my research) a 75mm equivalent on a DX body. Does anyone else have experience with using it in this way as a general-purpose (or “walk-around” or “always-on”) lens on DX?
Yes you are correct the 50mm on an DX body(D5100) will give you the field of view of a 75mm lens on an FX body.
Generally speaking, 75mm is somewhat tight as a general purpose walk around lens. 50mm is more commonly used for this, and to get that effective field of view on your camera you would want something around 33mm or so(which you already have in your 35mm lens).
You can find more information on why 50mm is so common and recommended in this thread: Why is the 50mm prime lens the most standard?
Keep in mind this is all down to personal preferences. Depending on your shooting style, you might find that 50mm is exactly what you love to shoot and you can shoot exactly what you want at all times with this. Myself, I find 50mm too limiting especially when indoors on a DX body, especially when I am trying to capture images of the faces of multiple people. It is simply too tight of a crop for my taste. Outside and walking around, a 50mm typically works out great on a DX body, but that is my opinion - and certainly up for debate.
This is absolutely a personal choice. Sure you can go around shooting anything and everything with a 50mm lens or a 35mm or 28mm... etc.
The one thing that works out nicely with a 50mm on a cropped-sensor is that you can usually shoot with both eyes open and have virtually no dis-junction between what your eyes see. This is great for doing street photography because you can see what is out of your frame quite clearly. For me it takes a 55mm to line-up perfectly but that is dependent on your viewfinder's magnification.