What is the name of your set?
Ekkremes
What is the core concept of your set?
"A world without mana rediscovers magic."
Basically, the mana of Ekkremes undergoes massive ebbs and flows, with millennia during which magic is barely possible at all and considered a myth by the populace, to times where it magic is as accessible and well-understood as on any normal plane. We are visiting right as the plane is on cusp of such a change.
Common designs:
1. Pendulum Engine {1}
Artifact — Contraption
{T}: Add {2} to your mana pool. Activate this ability only if a creature is attached to Pendulum Engine.
Operate {2} ({2}: Attach an unattached creature you control to this artifact, or unattach a creature from it. An attached creature can't attack or block. Operate only as a sorcery.)
Operate is a keyword representing solutions elaborated to problems that normally would be solved by magic.
This is an interesting idea. It says "steampunk" to me much more than "magic being rediscovered".
2. Entropic Siphon {3}{B}
Instant
Each opponent loses 2 life. You gain life equal to the life lost this way.
Rebate {B} (You may cast this spell for its Rebate cost. If you do, change its text by reducing all numbers by 1.)
Mana was not entirely absent from Ekkremes but casting spells was so difficult mages have had to settle for much smaller effect.
//I understand what you're going for flavor-wise, but the result is an unappealing wording. The card would be much more attractive like this:
Entropic Siphon
B
Instant
Each opponent loses 1 life. You gain life equal to the life lost this way.
Surge 3B (You may cast this spell for its Surge cost. If you do,
change its text by doubling all numbers.)//
3. Arcane Deductions {2}{U}{U}
Instant
Counter target spell unless its controller pays three colorless mana.
Latch 6 — {U} (If the last spell you cast this turn had a converted mana cost of 6 or more, you may cast this spell for its latch cost.)
This is an alternative cost-down mechanics since these are design ideas (and Rebate may be too similar to Overload), not all of which can be in the set together. It expresses a different aspect of the mana swell: once a spell has been cast, it becomes significantly easier to draw on the same mana to cast other spells.
As you say, these ideas really don't belong in the same set. I think this mechanic has some potential, but it certainly doesn't make sense on a counterspell. I also feel like the flavor isn't terribly clear.
4. Juniper Spirit {3}{W}
Enchantment Creature — Elemental
Creatures you control get +1/+1 as long as you control a green permanent.
Ethereal {1}{W} (You may cast this spell for its ethereal cost. If you do it enters the battlefield as an enchantment with no other types or subtypes.)
1/2
Another side effect of the mana swell is the return of these mythical creatures that could simply not survive in the virtual absence of mana during the ebb.
There are memory issues here; without any sort of physical representation, how does one know whether one of these sitting on the battlefield is ethereal or not? Also, Glorious Anthem effects are certainly not common. I like the basic idea, but the implementation isn't there yet.
5. Confounding Flautist {1}{R}{R}
Creature — Goblin Shaman
{R}, Sacrifice Demented Flautist: Counter target spell that targets one or more permanents you control.
1/1
Unlike Maro, I've always felt that Red, as the color that already messes most with your magic after blue, ought to be the the second color with counterspells. I also find it most appropriate that it is an enemy color to blue. This particular card is a near-colorshifted version of Hydromorph Guardian.
Far be it from me to disagree with a fellow color pie heretic, but whether or not this belongs in red, I don't know why it belongs in this set.
6. Partisan Saboteur {2/G}{2/G}
Creature — Human Mutant
When Partisan Saboteur enters the battlefield, you may destroy target artifact.
If only colorless mana was spent to cast Partisan Saboteur, it enters the battlefield with two +1/+1 counters on it.
2/2
Without magic, Ekkremes developed a significant amount of both colorless mana use and pollution. This result in a) the presence of monocolor hybrid mutants in the set and b) the relevant of colorless mana (already hinted with Arcane Deductions).
7. City
Land
A deck can have any number of cards named City.
This card is a basic land as long at it isn't on the battlefield.
{T}: Add {1} to your mana pool.
How will the player have a chance to get enough colorless mana for things like Partisan Saboteur's effect? This is how. Cities function basic lands except that it won't affect things like Domain or Coalition Victory.
This is a dangerous road to go down. For one thing, you're going to have to deal with the fact that most players don't know the difference between colorless mana and generic mana. (This is entirely Richard Garfield's fault for using THE EXACT SAME GODDAMN SYMBOL for both of them, but there it is.) Somehow, your cards have to be resilient to this potential for misunderstanding. And if you want to go with Barry's Land, it has to be a major part of the set- it's basically a sixth color.
Summary
There are a lot of mechanics here, and many of them have lots of potential for design space. It's not clear how they all fit together. In fact, it it'll probably be necessary to cut things down significantly before building them up again. Choose a mechanic, decide what cards fit around it, and then decide what sort of world it makes sense in. "World where mana is wacky" doesn't have a lot of resonance.