I would go Savage worlds. It has a lot of what you need. I must admit I have not played it much but I am about to start a campaign and I have been reading the rules for a few weeks now.
1 A sense of simulation that allows for handwaving but does not assume it.
I think SW is not a strong simulator, but it is fast and quite logical. The thing I like about the combat is the players can think of neat things to do (tricks) that can 'feel' like a sim, but in reality it has a simple core rule that encourages the player to describe the action in detail.
2. Math is fast.
Yes very fast.
3. Defender gets to actively roll to defend from being attacked.
Not so much here. There is an option to try a full defense action, which allows the player to roll for his defense, but it is only usefull in some situations, and the player can not move that turn. But the option is there and useful in certain situations.
4. Characters can grow in power to fight armies.
More as a leader, not really single handedly. Even at a early level you can comand squads of people. There are mass combat rules also.
5. Lots of minis without using lots of time.
Check, mini use is encouraged and the combat is relatively fast.
6. Being hit is bad, not assumed. The hits you don't dodge or soak should hurt.
Check on this too, you get three hits, each hit drops your ability to fight. But on the plus side, most NPC's only get one hit before they are out.
7. Any hit could kill but probably won’t unless the attacker outclasses the foe, in which case the foe probably will die.
Yes, for every 4 points damage over the targets toughness results in a wound. So you can get four wounds in one shot, especially with a large weapon or luck dice rolls (dice explode. Meaning on a roll of the die's max value, you get to roll it again and add them. So if you have a d6, and roll a 6 you roll again. If you get a 6 again you get to roll again, if you get a 1 you add them up for a total of 13 points off of a 'single' d6)
8. “Damage” is easy to track, but specific injuries are possible.
Yes only 3 wounds, easy to track, there can be called shots, and if you are incapacitated you can have a lasting injury.
9 Falling hurts
A bit. In SW normals will die from a 30 feet drop but it is unlikely a hero will.(A 10 yard fall is 2d6+5 points of damage. An average hero's toughness is 5-6 so a drop of 10 yards will cause
2 wounds on average. )But that can be solved by decreasing the fall increment from 5 points per 10 yards to 5 points per 20 feet! Up to you.
10 Magic is hazardous to the wielder.
I have not read the magic rules, so this I don't know.
11 Magic is not an “I Win” button or a guaranteed success.
See 10.
12 Character power not tied to gear.
Nope not unless you give them very cool gear.
Hope this helps.
JesterOC
p.s. OK I did some more math (well simulation more like it) on the falling damage issue (for my own curiosity). Turns out that on average a 30 foot fall will kill a PC 5% of the time (like rolling a 1 on a d20). However they will always be shaken (which means they can't move until they recover) and most of the time they will have two wounds.
This does NOT account for Bennies (a limited resource that PC's can use to soak up damage). So in actual play the chance of a PC dieing from a 30 foot fall is less.