Colossal armor is not going to fix it
Colossal armor is Spectacle, but once the idea has worn off the combat will be exactly the same. The PC's abilities to become giant and fight other giants will not really offer any difference in the way they fight. They could pick up and throw a building, but they could do the same thing on a smaller scale with a rock. Now if they were fighting giant, armor clad enemies as regular sized people things could certainly get interesting.
"Terrain is often of more value than bravery....Bravery is of more value than numbers." - Sun Tzu
Your original instinct to use terrain was right, terrain can and should shape every combat that occurs. If the party isn't using the terrain, the enemies certainly should. Anything with the intelligence level of a wild predator (like a wolf) or higher should be able to utilize the terrain in some way, sentient creatures and people should especially make use of it to gain advantage in combat. For example if your players are able to flank enemies that were behind cover those enemies should probably be Shaken as their safe position is now exposed.
Combat encounters are their own story vignettes
Too often people view action and story as being separate (this is an issue in books, films, and RPGs), that the two don't mix well. The opposite is in fact true. The best action scenes are those where plot development and characterization is actively ongoing. Likewise each combat should have its own mini story arc with a rise and fall in tension as it goes on. For example, the party has just arrived at an abandoned warehouse they suspect the enemies of using as safe-house. The party attacks them and they begin to lose numbers and start retreating, the party rushes forward to capitalize on this and finds themselves ambushed by reinforcements the enemies called in. Now they need to escape, they pull back into the warehouse and are followed, as they reach the other side they explode some fuel tanks and light the building on fire cutting off enemy pursuit as they disappear into the night.
Your first question is about half a GM problem, and half a player/PC problem. I've been on both sides of this issue: GMing for a character who had little reason to participate in the story with the other PCs, and playing a character who had no reason to participate in the story and every reason to run wildly in the other direction. In both situations, the solution has two parts:
The GM finds ways to include the PC in the plot.
It sounds like your group is already doing this, but for posterity: this means that the GM must look for ways to actively involve the PC in the story, by using their background hooks, talking to the player about what the character might find interesting, and otherwise looking for ways to help the character find motivation within the story to participate in the story.
You do need to be careful not to change the story or the game's focus so much that the other players begin to feel excluded or ignored, but this is a matter of understanding your group, finding a balance, and getting buy-in from the player of the problem PC. Which brings me to part 2 of the solution:
The player finds ways to include their character in the plot.
This is the much harder part of the solution: the player must meet the GM halfway, otherwise the game becomes "The Problem PC Show!" and no one else has fun. This may mean the player has to bend or tweak the character in some way - not enough to compromise the core of the character, but enough to keep them with the group when otherwise they wouldn't stay.
This is, admittedly, difficult to do. Some people are so attached to their characters that they're unwilling to compromise; or they simply can't see a way to bend the character on an issue without breaking them completely. However, it's absolutely required in order to solve this problem.
Why player buy-in makes a difference:
When I played a character who had no reason to participate in the story, I looked hard for ways to make her want to be there. But all logic dictated that she run far away, find a hole, and pull it in after herself, so any other choices felt wrong to me. This showed in my roleplaying, and ultimately caused much frustration for our whole group as session after session became centered around getting her involved when she didn't "want" to be.
I put "want" in quotes there for a reason. Players with especially strong "my guy" syndrome (which I know I'm prone to) will insist that they're "just playing their character" and that "the character can't be changed". But when I GMed for a character who had no reason to be there, his player was willing to meet me halfway, and the result was a fun campaign for everyone where that character even made a large part of the highlight reel.
The reason it worked was because the player was willing to say, "he has no reason to come along, but does anyway, because that's how group-based RPGs work." We hand-waved it a bit as "he has nowhere else to go and nothing better to do", but really that character should have been as long-gone as mine wanted to be. But because the player was willing to take the meta option and bend his character enough to say "screw it, he's participating" without looking for a story reason, it worked. It kept the game from focusing too much on that character, but meant he was still there when story developments happened that he was interested in, thus giving him the time he needed to organically grow interested in the plot.
When the player isn't interested in the scenario
This part is a little trickier. If the player doesn't buy Dresden's world, including all the magic elements, what's he doing playing a Dresden Files game anyway? You and your co-GM need to talk to this guy privately, out of game, and ask him why he's playing. If he just wants to hang out with your group and doesn't care much about the game, then you need to address that. Maybe give him a character with a minor support role, so that he doesn't need to participate much in the game and can just hang out; maybe say that if he just wants to hang out, the game isn't the time for it and you'll find other group activities he can participate in. It's up to you and your group to decide what's best here.
If he insists that he wants to play the game, then you need to find out why he's actively sabotaging it. Tell him that his actions suggest he doesn't want to play, and in fact are making it harder to play. It's possible you simply have an attention hog on your hands, in which case you should deal with him appropriately. (I'd suggest going through the problem-players tag, as there are a number of questions and answers you may find relevant depending on your exact situation.)
TL;DR: The GM and the player need to meet halfway on adapting the character and the world. But if the player isn't buying the game's scenario in the first place, then that must be addressed first.
Best Answer
General advice for any issue with a trouble player is to talk with them and clearly explain the trouble that you are facing. You should definitely explain the problems you are having with trying to keep track of all the custom stuff and see if the two of you can find a solution. However since this is a question specifically about Savage Worlds, I figured I'd address your specific concerns in relation to the system.
You mentioned that you are both a new GM and new to Savage Worlds. One thing that the creators of Savage Worlds often say is that although it's tempting to play with customizations right off the bat, you should really try to play "by the rules" first. There's a great section in the GM section about Edges and Hindrances that encapsulates this pretty well:
Replace "Edges and Hindrances" with "Gear" in that sentence and I think the same advice applies. It's tempting to add all sorts of new gear, but at the end of the day you're probably just as well taking the stuff from either the core book or a published setting book for the setting you are playing in.
You didn't say what setting you were playing in, but since you listed some modern weapons, I'm going to guess you're playing in that time period. In that case, there shouldn't be any real reason to create custom weapons because there are so many in the core rules. But notice that there are very few "unique" weapons", especially in the modern era category. All of the guns have roughly the same damage, rate of fire, shots, and special notes. For instance, all assault rifles deal either 2d8 or 2d8+1 damage, have a rate of fire of 3, have 20 or 30 shots, and have AP 2, auto-fire, and possibly 3-round-burst. If you want a new assualt rifle, all you really have to do is pick one of the ones on the table or mix a few of their stats and slap a new name on it, then pick a cost and weight for it.
I've worked on some third party Savage Worlds products and in all honesty this is exactly what most Savage Worlds writers do for anything that isn't groundbreakingly different (and if it is, we usually just add an extended notes section explaining what it does). We do this because we know the numbers already work and because we want to match player expectations. Say that I was creating a setting that had an LSAT rifle (a potential replacement for the M16 used in the US Army today). I'd just pick the M-16 stats and change the weight to be lighter. That's it; there's no real reason to customize further. You seemed to have the same idea for this with your bangstick you mentioned at the end. Just have him buy a bangstick for a price that seems reasonable for the setting, then change the weight and any essential trappings and you're good.
It sounds to me like there might be a bigger problem too in that your player is trying so many different things. Shields, shotguns, pistols, grenades, knives, bangsticks, and dogs. Again, I don't know what your setting is, but it might be appropriate to start enforcing consequences with all that. How is he hauling all this stuff around (if you want to use the encumbrance rules, what penalties is he taking)? Does he freak out every person in town when he comes armed to the teeth with these weapons? Do people not take him seriously when he has a pistol and shield? How much in debt is he to pay for all these different weapons each with their own ammo? Where the heck did he find a shield in a time when people are toting around guns?
You did note that he was starting to be spread out pretty thinly, so you might also want to encourage the player to start specializing in a more limited set of gear and stick with it, saving his other ideas for a different character. Moreso than in Dungeons & Dragons, there's not much point to continually upgrading gear since those in the same category have basically the same stats and there are tradeoffs between different types. Also depending on the setting it may not make sense to switch weapons (if you're playing a military game, you're probably staying with whatever you were assigned by the higher ups).
Also one last thing: you said that the character had a shield and guns. Having a shield is pretty much worthless in a modern game because all guns have armor piercing. He can carry around a Medium Shield for an extra 12 weight to get +1 Parry and +2 Armor vs. ranged attacks, but it's unlikely that he'll get into melee combat (why bring a knife to a gun fight?) and all rifles have Armor Piercing 2, which will go straight through it as if it weren't there. It would provide 1 point of Armor against pistols, which generally have Armor Piercing 1, but is it really worth carrying a shield around, not to mention tying up a hand that would prevent you from using a shotgun or rifle, just for that? There's a reason that soldiers historically quit carrying around shields once gunpowder weapons were invented.