Well that was a nice read! I will try my best to answer some of your questions.
First of all, I see exactly what you mean with the title and colours, many people don't like the fact that staff cannot be distinguished from other players, and the group-related colours become a whole lot more unrelated. Although others don't really mind, I myself am one of those people.
If we implemented a new currency system like how Lava has cookies and TNT with its points, how would we work it out?
How would players acquire it?
Should it be per Kill, or per round survived?
Would kill streaks by Zombies have any affect on the matter? (Streaks = "Dominating," "Godly," "etc.")
How would is balance out? Will eating humans be a more effective means of getting these points to spend in the shop? Or would being a human would?
You could design the rewards system in multiple ways. The most common method across the board of zombie survival servers is to be rewarded when you survive a round. Ranging from complex algorithms to simple if/else queries, it is possible to modify the reward based on factors such as map size, round length, total survivors left, total round players. For example, a short round on a huge map with 7 survivors - minimal rewards. Be the last one alive on a small map with a long round length? That is where the jackpot is at. You can also implement kill streak rewards so the zombies aren't ultimately left out of the situation.
Additionally, Can power-ups, such as the invisibility idea EVEN BE IMPLEMENTED into the server?
If I recall correctly, any form of attempt to have a skin to make a player invisible has always ended up with a player bathed fully in white.
Yes, it is very simple. You don't need a skin, you just take the player from the server (don't send players their position/appearance). This is what happens when you /hide. A timer could be made to last 30 seconds, once up, the player becomes visible again to everybody surrounding them.
But again: What kinds of power-ups could even work on the server?
There are infinite ideas awaiting to be found. Lets think of some right now;
Invisibility - 30 seconds.
Invincibility to infection - 30 seconds.
A pillar-block - Place a block which forms a pillar to the top of the map - you spawn on the top.
A gun - You could purchase bullets for the gun. If you are human and shoot zombies, it sends them to spawn.
A grapple - Zombies could grapple a human to get them closer.
A random teleport - When purchased the player could use a command to teleport themself to a random passable X Y and Z in the map (air/water blocks).
Flying Platform - Could allow a player to use for 10 seconds, but allow all players to see their platform, so hacks cannot be mistaken for.
These are just some ideas for power ups, there are hundreds you could think of and implement.
a player can buy a good number of these power-ups, and just keep spamming it whenever the time limit runs out
Very easily combated with restrictions on items, and the prices they are set at. I'll take two examples.
Life - A life could only be purchased once in a round. It would be un-purchasable after the point in time where there is 2-3 minutes remaining for the round.
Gun - Bullets for the gun could be very expensive. Only a maximum of 10 bullets could be used in a round. A command (/allowguns) can enable/disable the usage of them if staff think they are abused.
All in all: I'm not that supportive of the idea.
I respect your opinion, many people would agree with you. But think of the benefits of a well-designed store and put them next to some disadvantages, which way does the scale go? That is something your community's developers/owners would have to think about if you were to take this idea and go forth with it. Personally I think a store would give players even more of an incentive and make the game even more enjoyable than it already is.
