Your game will focus on certain activities, and those will take up most of the time. It looks like a lot of this game could be combat and exploration. You want to minimize how many rolls and how often the player looks at the character sheet during these activities.
Stats
Please name Stamina as Endurance, and name Social as Charisma. I know it's cliche, but there's a reason.
STR, AGI, END, INT, CHA, PER
STR, AGI, STA, INT, SOC, PER
The second one has an awful lot of S-abbreviations. And you can actually abbreviate to one letter if all your stats start with different ones.
Initiative
I'd suggest for Initiative, a straight d6 + Agil. Ties go around the table starting with the person to the left of the referee. Yes, that means if the referee ties with a player, the player always goes first.
Or, d6+Agil but ties happen simultaneously. That means two people could attack each other and both hit, killing each other at the same time. Or someone could start a train and begin to move away on it, and the other boards the train at the same time.
Attack Roll
Using Agil for the target number for attacks looks good. But it does make Agil pretty important. I'd suggest making Initiative based off Intelligence instead, to help prevent it becoming a dump stat. Of course, Initiative isn't that important because everyone gets to go once each anyway.
STR for melee and PER for ranged are good choices.
Dodge/Block
The dodge/block rules are complex, requires a back-and-forth between the attacker and defender, and aren't that useful in a fight with multiple opponents. I'd suggest simply a "stance" rule where you can fight with an offensive or defensive or middle stance in any round. On your turn you decide, and the modifiers apply until you change your stance on your next turn.
Offensive: apply your entire Agil to attack rolls. No running.
Defensive: target number to hit you is 3x agil (instead of 2.5x). If you have a weapon you gain 0.5x and a shield gains you 0.5x. No running.
Middle: Run becomes possible (Run should be 5x walk move).
I suggest against making different dodge/block rules for ranged attacks. Yeah I know people have a harder time dodging bullets. But this is a place where making a concession to gameplay at the cost of realism is okay.
Cover works okay, I'd suggest that cover is +1 (1/3), +3 (1/3) or +4 (3/4) without the returning-fire cover reduction. You just can't return fire with 100% cover unless you have a little firing port or something. Make a note that cover applies against ranged and melee, but that sometimes a melee attacker can move around the cover.
Critical Hits
Rolling a critical hit determination check is clunky, but neccessary if you're on 1d6. You just don't want crits to come in every 6 attacks. The chance of a crit with your rules is 1 in 36, which works okay.
Beware using 2d6 for your critical hit table. Two dice gives you a mountain-shaped graph of probabilities, and three gives you a bell curve. Simply put, the middle numbers will come up a heck of a lot more often. You're better off using a single larger die, or else put the more common criticals in the middle. If you're careful, you can assign a larger number range to the low and high rolls, making the probabilities even. Something like:
Roll Critical Hit
2-4 Hand
5-6 Arm
7 Head
8 Leg
9-10 Knee
11-12 Eye
But even that is going to be kind of off. And I couldn't fit Neck on there. 1d8 with 8 = Attacker Choice would be lovely.
Movement
No movement section? Humans walk about 2.2 MPH, but since you're using metric you'll need to convert. 6-second combat rounds work well if you have firearms and melee, but you might want to give Semi-Auto guns two attacks per round. Base your human movement on that 19.36 feet per 6 seconds walk speed.
Jog / run should be a LOT faster. Just hustling a bit should give you double. x3 for jog and x5 for run would be okay for fighting rules. You don't want people scurrying all the way across the map in 6 seconds.
Called Shots
Unless you're absolutely married to this idea, I'd advise against it. Players quickly figure out the optimal selection, usually it'll end up being hits to the head or (if nerfed) to the hands. It also slows down the game like crazy because you have to add up the situational modifiers, check for armor location, check for special effects, in addition to the normal combat procedure.
A combat system without called shots assumes that the attacker chooses the best possible target. We assume people are hitting each other in the head. This is why helmets are so important.
I'd suggest putting your Called Shots results in your Critical Hits table instead.
The "head struck - dazed" effect is going to be difficult to handle in a game. Not only is it a modifier to a stat that is used dozens of times per combat round, the penalty changes every round, and there is a check to resist it that involves quick subtractive math. Every single one of these things will slow the thing down. I suggest instead:
"Head Struck. Roll a Stamina Check. If you fail, you are dazed for 1d6 rounds. Being dazed gives you -1 to all your rolls. If you are dazed again before it ends, you fall unconscious for 2d6 rounds instead."
And drop the "double damage, quadruple from firearms". Dazing is a big enough bonus for the meager headshot attack penalty, and there is absolutely no reason to give a different damage multiplier for firearms in any case. They get higher base damage, so their multiplied damage will also be higher. Also drop the called shot penalties with larger weapons, I'm not sure that makes any sense and it clogs things up.
The same thing goes with the individual attack location effects. If you really want those, drop them on the Critical Hit table.
Stamina Roll? (Pg5)
You mention a Stamina Roll but don't explain what that is. I assume it's a roll of 1d6, trying to get under your Stamina stat. Right?
Damage
I like the defender choosing to use up Stamina to soak damage. I'd suggest that this Stamina damage cannot be healed normally and you need a doctor, tech, or magic to do it. That makes it a meaningful choice - otherwise you would always burn Stamina when you needed to. I'd leave off using Agil or Strength, but I could see why you would want to. But leave those at the same 3:1 ratio just for ease of use.
Dying
On one hand, players don't want to die all the time. On the other, they don't want to sit there rolling to see how long it takes them to die.
I'd suggest the following:
"Once you fall to zero or below Life Pool, you fall unconscious. Non-Lethal damage (blunt, unarmed, some poisons, etc) can't kill you, but Lethal damage can. If some of your damage was Non-Lethal, you just fall unconscious. But if it was all Lethal, you begin dying.
When dying, every 10 minutes, you take a point of Lethal damage. If you are revived by a doctor, even if he doesn't heal your damage, you will stop dying. If you are hit for more damage after reviving, you fall unconscious again immediately and might begin dying again.
If your Life Pool ever falls to the negative of your maximum (-5 for Humans, because they have 5 Life to start with) you immediately die.
Non-Lethal attacks cause Lethal damage to unconscious people.
Professions
I'd take off the Crafting bonus from Architect. Architects don't always actually build things.
Psychiatrists probably shouldn't get the same Medical bonus that Paramedics and Doctors get ... maybe +1 Persuasion and +1 Academics instead?
Student should probably get +1 Academics and +1 Salvage instead of +2 Salvage.
Farmer should get +2 Agriculture instead of +2 Crafting.
General Editing Notes
Go over your text carefully and make sure you're using the same structure choices. So if you do present tense, third person, active voice, etc. make sure you don't deviate. I find that referring to the reader as "you" and using the active voice really cuts down the word count and makes things read clearly.
Also, specifically state what they can do and assume that unless it says they can do it, they can't, and it's a referee call. For example, when speaking of damage, you could simply say:
"You can sacrifice points from your Strength, Agility, and Stamina to avoid damage, soaking up 3 damage per statistic point."
You don't need to mention that you can't use Perception, Intelligence, or Social for this. It's clear that you can't, for the same reason it's clear you can't burn skill points to do the same thing.
EDIT: My dying rule suggestion has an unintended consequence. You smack yourself in the face to take 1 point of Non-Lethal, which means you can jump off a cliff and you won't die - you'll just fall unconscious. I wanted to include something to the effect of "If your lethal damage alone is enough to put you at 0, you begin dying) but it sounded clunky.
So that would need work.