I like the approach here. Here is some initial feedback, mostly on the guns (I didn't read the part on explosives yet). It's heavily colored by my own pet peeves about RPG firearm stats.
1) The damage is too high. I don't see why being shot with a 9mm round is equally as damaging as being cleft in twain with a greatsword. Seriously, picture a greatsword, and it's cutting your guts open. Now picture a 9mm round, and it's shooting you someplace other than the brain, heart, or major artery. I'm not saying bullets can't be deadly; I'm saying that the things which make them deadly are not well represented by simply having a high damage number.
Now the really big guns might exceed melee weapon damage. I'd be willing to accept that an antimaterial rifle is more lethal than a greatsword. Ditto for something like a mounted gun. I'd probably put the bigger hunting rifles, or a 12-gauge at close range, about on par with the greatsword.
2) Now, one of the things that DOES make modern guns deadly is their rate of fire, especially compared to bows and crossbows. If you're good, you can fire a bow several times in a round. But with even a basic handgun and modest training, you can shot that thing several times in a round, and potentially even hit someone if they are close enough. And for weapons with full auto, or machine guns, it's even worse for the victim. BUT doing that chews through ammo!
My suggestion is to blatantly steal from Savage Worlds: Make each gun's base damage modest, and then let the shooter expend extra ammo to get bonus damage. For example, maybe a 9mm is a 1d6 weapon, but if you spray out 3 rounds, it goes up to 2d6. Maybe an M-16 deals 1d8 damage, but you can fire a 3-round burst for 2d8 damage, or a 15-round burst for 3d8 damage! That's a pretty significant ammo expenditure, if you're tracking ammo.
3) The ranges are very good for game-play but they seem short compared to real-world ranges. I think I'd fix this with another special action. If you spend an action to Aim, your range is doubled for a handgun or SMG, or tripled for a rifle. This stacks with a scope. This represents that snipers really can take a long time to line up a shot. A single action is not super realistic, but I think most players would get the idea right away.
4) I like systems where shotgun spread causes its damage to decrease slightly at range. (I don't subscribe to the RPG wisdom that the shotgun's spread makes it much easier to hit. Or if it does, it also reduces damage, since you'd not be hitting with the full load. I guess the factors involved in firearm accuracy are complex, and I'm not convinced that the shotgun's spread is significant enough to provide any bonus, at the coarse level of D&D mechanics.) In 5e terms, I think the way I'd do this is at long range, the shotgun has "disadvantage" on damage -- roll twice and take the lower damage. So you might still manage to hit someone with the full load at range, but it's less likely.