Never C-betting with air.

[PokrLikeItsProse]

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not Cbetting is 0EV.

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No, folding is worth 0. Checking does not mean you lose the pot. Comparing a continuation bet with folding will strongly bias your analysis in favor of making continuation bets, even when they are less profitable than the alternatives.

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Folding is deffinatly worth 0EV, however checking is a different story. Checking could actually be close to -EV.

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Checking can never have a lower EV than folding. The strategy of checking with plans of not putting in any future bets (that is, checking behind on future streets if checked to and folding to any bet) dominates the strategy of folding, so one should obviously never just fold if checked to on the flop. Folding has an EV of O. Checking with plans of not putting in any future bets into the pot must be worth at least 0. In fact, it is worth slightly more because you sometimes win when the pot is checked down all the way.