Alright...but your asking me for help. Have fun
Grammar:
First out of them all, don't double space the effects please. I'm aware that you don't like the bulkiness of card text, but yet some of your cards have it, which kinda makes no sense, such as, Network Swords Woman, Network Assault Team, Network Swordsman, and especially Network City, just to name a few. Also make sure that you properly capitalize "Battle Phase", "Damage Step", as well as other parts of the field such as, "Deck", "Main Monster Zone", "Extra Monster Zone", etc... Next, a colon, (:) is used for conditional effects, such as, "When this card is Normal Summoned or Special Summoned:(effect)". As an example of one of your cards, Network Air Defense System, "effects do not activate at this time) destroy all WIND monsters on the field; then Special Summon a "Network" monster from your hand or deck whos level is equal to or less than the number of WIND monsters that were destroyed by this effect." You did this correctly with, Network Assault Team, "If your opponent controls more monsters than you do:"... Moving on, the effect of Network Swordsman should be reworded. Its' effect currently reads, If you send both this card and "Network Swordswoman" for a Link Summon"... But in my opinion, it should say "...if you tribute both"... The effect of Network City should say, "Each time you summon a "Network" monster"... Not, " Each time you summon a "Network" card"... Or just reword the entirety of Network City. It is incredibly bulky, and so much to read. If you can find a way to sum it up, that will work as well. The effect of Network Generator is also way to wordy. If you can find a way to shorten it, that will be great. "Other" in the effect of Network Defender Golem should be lowercase. The effect of Network Demon can be summed up by just saying, "...your opponents Spell or Trap effects.". Reword the entirety of Network Giant. It is way too confusing to understand.
-whos = whose
-Swordswoman = Swords Woman
Cards:
I agree with Debt on the Link arrows. You can have them do something else then just harming your opponent.
Network Mercenary: It's effect is a little strong for a monster you can just freely summon for it being just a level 3.
Network Samurai: Same thing as before, small monster, but a strong effect. Other monsters may be small and have good effects, but the effect you gave it is too strong for its' level.
Network Swordsman & Network Swords Women: The last effect of the monster kinda makes no sense, you can make it so it counts as 2 tributes.
Network Synthesis Soldier: For it being a level 2 monster and having that kind of effect is a little strong. I am finding a pattern here.
Network City: The counter mechanic is fine with what the deck does, but having it just be active with the number of counters it has is a little strong. If you make it so you have to spend the counters like what Gateway of the Six does, it may be a little more balanced.
Network City 2: Same thing with Network City, just have it so you have to spend counters for the effect for balancing.
Network Generator: I'll give you credit for it being unique, but its' effect is really strong, for no cost. When you destroy a defense position monster, you just negate its' effect just like that. Having a cost would be nice for balancing.
Network Invasion: It has a cost of skipping your normal Draw Phase, but because you can destroy a card on the field AND you can just get it back next turn, makes it OP, and spammable.
Network Gustav Cannon: Just like Debt said, its' just a better Solemn Strike.
Network Railgun: The cost is fine, but having the effect be negated for the rest of the duel is a little too much, and too powerful.
Network System Crash: I agree with Debt again, just a better Tools of the Bandit
Network Paralyzing Machine: Just a plain OP card with no cost what so ever. Yes, you do only run 1 copy, but if you play it, I literally cannot play the game unless I find a way to destroy it.
Network Shield: Again, I agree with Debt, it's just Mirror Force
Network Angel: It can attack 3 times, negates effects of monsters it points to, AND if i deal damage involving the card is cut in half. If you really want to use something with these effects, I say just pick one, and if you want to use the multi-attack effect, make it have a good cost because right now, it's just free.
Network Defender Golem: The fact it cannot be targeted or destroyed is a good effect. But because the only option I have is to beat over it when it has 3000 atk, is much. But I do like how players take no battle dmg involving the monster.
Network Demon: I understand that you have to use 6 monsters as tribute, but because it negates effects in 3 monster zones it a little much in my opinion. And it makes it so Network cards can attack me directly. AND they can't be effected by spells and traps. If you want to make it powerful, only limit it to maybe 2 of the 4 you have, or add costs. I know you can say "it needs 6 monsters is enough of a cost." but because of how much you summon, not really.
Network Marine: If my monster is going to be equipped to your monster, it has to go on your side of the field. If you can give me 5 examples of other cards that don't do this, I'll be fine with it.
Network War Samurai: Well first of all, you can't even use it. It need 2 Network monsters, but it's a LINK -3 monster? Now, if it said 2+ "Network monsters, that's fine. The only reason I will let the effect pass for this monster, is because it's atk isn't really high.