You can't just select a distance and have a mic magically reject everything else. The only thing you can do is get the mic closer to what you want to record, or switch to a less sensitive microphone type such as a dynamic rather than condenser. However, due to being less sensitive you need dynamic mics close. These are the kinds of mics singers use, or the kind of headsets that news helicopter reporters wear.
Things like noise gates are indiscriminate. You talking quietly gets rejected the same as the unwanted noise because all it does is pick a volume and reject everything under it.
Any mic will pick up handling and cable noise. Less sensitive mics like dynamics are less susceptible but it's still there. If you want to eliminate it you need to secure and isolate the microphone. Things like cable clips for lavs and headsets, shock mounts for other mics, routing cables differently so you can move without dragging on them.
From what you're saying you want, something like this would work. Shure WH20QTR Dynamic Headset Microphones https://www.amazon.ca/dp/B0002F6OY4/ref=cm_sw_r_cp_apa_sT81BbTJZP93N