My answer, which gets to most of what you're looking for, at least, is Burning Wheel.
low fantasy (where magic is very rare or virtually non-existent)
Burning Wheel has a magic system but it's entirely optional, and if you do choose to play with it you will notice that a. it's not terribly useful in combat, and b. failures to cast spells can have some pretty nasty consequences.
grim theme (dirty, gloomy, death on every corner)
This is one arena where I think BW maybe doesn't quite deliver; it's not necessarily easy to kill a character, particularly an established one. In fact, if a player has an extra Deeds point sitting around and their character is mortally wounded, they can spend that point and save them.
That being said, it is very easy for a character to get seriously maimed in this game and in effect take them out of action. In fact, in the case of the mortal wound, spending that point doesn't make your character instantly healed. Depending on their stats and how well they roll their saves, it can take years to heal up all the way from a mortal wound.
And the best thing about this is, there is basically a chance that a mortal wound can be inflicted in every combat your players decide to engage in. Most BW players figure out very, very quickly that combat is not a thing that they do unless they absolutely have to because chances are, somebody they like is going to get hurt badly.
Additionally, there is this concept of Steel which is missing from a lot of games. Basically, Steel is a character's ability to do something really brave or just plain suicidal without chickening out. You roll Steel when you get wounded, when you try to run straight at a guy 200 feet away who's pointing a cocked bow at you, when some big bad threatens you, and so on. If you fail the roll, you can actually choose what your character does, although the choices are things like "cower and possibly pee your pants" and "drop whatever you have in your hands and run away screaming".
classless system (i.e. letting the player construct their own characters)
Not only is BW classless, using the system of Lifepaths that they have, coupled with Luke Crane's amazing amount of research into medieval life (and, where it applies, the Tolkien mythos), you can create virtually any character you want. I played one campaign as a lawyer and agitator for equal rights for serfs. He was born noble but when he grew up, instead of becoming a knight like his parents wanted him to, he went into law instead (along the way I gave him some skill in mace wielding because hey, you gotta do something in fights). All this was part of the character creation process.
mundane, NOT heroic (i.e. not letting the players become some demigods and such - keeping it human)
BW models itself after Tolkien, which means that humans can be regular old Joes or studs depending on how many Lifepaths you allow characters to have at the start of the game and how you choose to GM. Elves and Dwarves are OP just the same as they are in the LotR series, but if you restrict players from playing them or just ban them altogether, things can be as mundane as you want them to be.
rich in combat and tactics (as in putting together a custom set of armor with its pros and cons, choosing a specific weapon with its pros and cons (speed, reach, style, types of damage), smithing and crafting, learning combat moves and such)
You can be a weaponsmith in BW but where I think the system truly shines is in its variety of tactics available in combat. There are separate systems for melee, ranged combat, spellcasting, and even debate (no, seriously, it's resolved like a little combat system itself and it's kind of awesome). There are a crap-ton of options available to you in melee, for example, from choosing to all-out strike in a turn to parrying (you script out around 10 seconds worth of moves at a time and you generally have an idea of when your opponent is going to strike due to speed scores, so this can make some sense), to a "counter" move where you choose to allocate dice between attack and defense at the moment the attack is resolved (the downside to this being, even if your opponent doesn't attack, you still have to put at least one die in defense), to spending the move trying to move out of dagger range and into, say, sword range if that's what you're carrying, and so on.
Weapons behave like weapons ought to behave. If you decide to wield a bow in melee combat, you're going to get one shot off if you managed to cock your bow ahead of time and that's generally it. As noted before, there are significant advantages to wielding a polearm, not to mention the huge disadvantage that if someone is quick enough to get inside your range, that fancy polearm is now basically a club. You won't be able to use a mace as often as you can use a sword or a dagger. To simulate the kind of expertise that advanced martial artists have, you, as noted before, script out your moves ahead of time, and although you can cancel out of a move during resolution there are some serious consequences for doing so.
customization-friendly (as in keeping the system a bit abstract and flexible - i.e. not swaying into too much simulationism and specifics, in the Riddle of Steel sense)
This is probably the biggest drawback to what you're looking for because in my experience BW is about as simulationist as games get. I don't think it's that hard to do combat once you've gotten the hang of it, but there is a learning curve (hint: print out and laminate an action sheet for every player so that they can just check the boxes they want to use with a marker instead of writing stuff down every turn or, worse, going around the table DnD style).
dice pool resolution mechanics
This is exactly what BW uses. If you have a 4B strength, you literally get 4 dice to roll and when it comes time to succeed or fail at something you roll them and count successes (for "B" or "black" you have to roll 4-6 to succeed). You get additional dice for skills, and depending on circumstances you might be able to have another player aid you by rolling a die of their own or add an extra die to your pool via the use of FORKs (Fields of Related Knowledge; for example, if you're trying to pick an ancient Dwarven lock, you'd probably be testing Lockpicking but you might just be able to FORK to Dwarven History to add an extra die or two).
level-less system (a point-buy system would be desired - as in taking certain points of experience for enemies defeated and/or quests solved, and spending these points on the go / whenever one feels like it)
BW doesn't use a point buy system. What it uses instead is a system similar, actually, to the Elder Scrolls series. That is, you increase skills by using them. In fact, once you get a bit of proficiency, the only way you can increase your skills is by trying really hard things that are in some cases statistically impossible and somehow succeeding at them (via helper dice, for example, or by spending artha (think FATE points) on re-rolls and "open ended dice", which allow you to roll an extra die for every 6 you get).
This is actually not as tough to keep track of as it sounds. The trick is that the players have to do it.
rich on thievery (sneakin', stabbin', stealin', shootin' ... but still, I may be able to house-rule these features into the system myself)
You can include as much thievery as you want. There are whole groups of lifepaths devoted to thievery, and there are lots and lots of ways to create a thief or a burglar or a forger or a con artist or (insert thief type you want to play here). BW doesn't have specific mechanics outside of skill testing for thievery, but then, the skill testing mechanic is quite rich already.