When you take damage in life, it doesn't normally take 20 minutes to heal 'no matter the damage'. In minecraft, Falling off a 10 block high building heals just as much as fast as sinking into lava for a bit. My idea is that taking damage from different sources should take different amounts of time to heal.

For example, if I got hit with a diamond sword than the 3-5 hearts of damage you took should take half a minecraft day. It's just a cut. But, if you got blown up by a creeper, it would take 2-3 days due to internal injuries from the shockwaves. Getting a little closer to the creeper would make it take a little longer to heal, as well.

It should be a little dynamic, what I mean by that is hearts taken from some stuff shouldn't interfere with hearts taken from other. If I got blown up by a creeper for 3 hearts of damage, me being a little safe to run away, it would take about 2 minecraft days for those three hearts to heal completely (Not instantly). If, say, I took a little damage during that time (got shot with a bow for 2 hearts), it would take me 2 minutes to heal those two hearts completely, while the damage I took from creepers is still healing.

Hunger shouldn't have an affect on healing.

Another example would be if I fought a zombie. In all, the zombie took 4 hearts of damage. In about 4 IRL minutes, half a heart would heal. Then another half-heart in 4 more minutes, etc, until a day passes in minecraft that the hearts I lost from the zombie heal completely.

Lava, on the other hand, is serious. All damage I took from lava takes almost forever to heal, and 30% of the hearts I lost in lava will never heal. The fire damage I took in lava will take about 7-12 days in minecraft to heal completely. If I take any fall damage in that time, say 4 blocks of fall damage (half a heart), that half-heart will heal pretty quickly since it's just a little bruise from the impact.

This is a little bit more simplistic than the last. If you hit a cow and give him 1 heart of damage, all cows in about a 4 block radius will walk away from you. If the cow recieves a critical 4-5 hearts of damage, any cow within a 20 block radius will start to run specificially away from the area the cow was from. Cows within 4-6 blocks will recognize you from when you killed another cow and will naturally want to stay away until they forget what you did.
Chickens naturally want to stay away from you, pigs don't care, sheep run away from you if you sheared them (and will recognize it's you if you sheared them), and whatever else you want to think of. Mobs will instinctively try to find shelter out of the rain.

A little more complicated than the last, but I like this idea.

Zombies will be a little curious around light sources and sound. If there's a torch around in their field of view and they're currently not attacking anyone, they'll go check it out. Same goes with if an anvil fell, if a block was broken/placed nearby (especially glass, longer range of hearing it break), if something jumped in the water, etc. They'll go near whatever made the sound, check it out, and just mind their own business after that. Zombies will hang around lightsources, though, sometimes looking at it.

The zombies go only for players that are in their field of view. If a player hides behind a corner, the zombie will obviously go to the last position he saw the player. If the player was able to shift/walk away silently without the zombie hearing him, he could hide behind something else while the zombies checks out where he was last. If the player places a block while he's behind the wall, the zombie won't immediately start running towards him - the zombie doesn't know he's there. He'll slowly walk to the source of the sound (if he can even be bothered to do that), check out a little around the block, and then mind his own business. If he sees a player, he'll chase after it - alerting a few nearby zombies.

As long as the player isn't in their field of view, a player can shift up to the zombie about 3 blocks close to them or even behind a wall. If he runs, depending on the surface he's running on zombies will go to wherever they last heard the running sound. Just because they can hear you doesn't mean they've noticed you.

The amount of oxygen in the area you're in now matters. The lower you go down, the less oxygen there is and the more dizzy you can feel. If you're inside of a pocket of air (3x3 hole you built yourself in underground), you'll eventually run out of oxygen and become dizzy. Torches use x0.5 the amount of oxygen you use, and will start dimming when there's not enough oxygen in the area and will eventually go out. Enderman and Creeper breath oxygen just as much as the player, too. "Air" goes through transparent blocks, so don't worry if your house is sealed off with nothing but a door. Since there's now a "Burnt Out Torch" block, torches might as well go out in the ran as well.