In real life you don't slide forward a few feet every time a dog "nudges" you. If I were standing at a cliff edge I could take most dogs nudging against me with falling forward off the cliff. They usually also approach your side or front, they don't ram into your back.
In real life, you can't walk on thin air.
Try it in Skyrim. There's a rock up on high Hrothgar where you can stand apparently fully unsupported.
In real life, you can't have only one toe standing on a rock, have the rest of your body hanging in free space, and remain standing on the rock as if you were standing on a horizontal solid surface.
Try it in Skyrim.
In real life, you can lose your balance and fall. You can still be in contact with the surface you are standing on. In Skyrim, this doesn't happen.
We can play this game all day.

Oh, and we have a terrier. The terrier has a lovely habit of nudging you in the knee with its nose. And yes, a very small movement of your knee is all that is required for the knee to buckle. And after that knee is buckled, and no weight is being put on it, the body reacts by changing how its mass is distributed over its center of mass. Which can cause you to overbalance and have to reach for the pole supporting the roof above the deck to prevent you from falling off said deck.
Or, as happened in one case, that small movement was all that was needed for an elderly relative to overbalance and fall off the deck, breaking their arm.
Dead is Dead.
Reload.
Yeah, sorry, even with my cousin's great dane, he doesn't nudge me so hard it shoves me 5 inches.
See above.
At your concern about NPC interactions with the player - in my opinion that is to prevent the player pushing passive people off ledges to murder them and avoid a bounty, rather than killing them directly. NPCs interact with the player because the player can generally do something about it if passive interactions are going to cause them to fall to their deaths. The two way interaction could be seen in Oblivion. It was removed in Skyrim to only be one way.
I.e. Not a glitch.