Yeah don't give villain easy opportunities to exploit you right off the bat.

Yes. At any one point, villain's range can be divided into several parts depending on your action.
If you bet...
Villain has a folding range (air), a calling range (mid-strength), and a raising range (monsters and maybe some bluffs).
If you check...
He has a betting range (value and bluffs), and a check-back range (mid strength and air that he won't bluff).

Working out how to maximise your EV depends on how accurately you range your opponent, and how well you "guess" his reaction to your action. If someone's range is mostly made of worse hands that will fold when you bet for value, you should often check to induce bluffs. If his range is full of worse hands that will call, you should bet for value.
Conversely, if you have a weak hand, you should bet it as a bluff if you think villain will fold, but you should check-fold if you don't think you have any fold equity.
With your mid-strength hands (and sometimes two pairs is in this category), you have a very good bluff-catcher, so check-calling (on the river) is often the best choice. Check to induce the bluff, snap it off, profit.

No. Why? This one too works: "winners checks with best hand and looser bets".

Everything in poker is true and false at the same time. Poker is a balance. When something is too true, then it becomes false. When something is too false, then it becomes true.

Perhaps what you want to say is: "you have to be as aggressive as it is sound to be". Because this both respects the balance and maximise your gains.

Can you elaborate on bluff catchers. Why are mid range hands good bluff catchers?

weak hands lose to some bluffs and therefore aren't good to catch bluffs with
strong hands beat some value hands and therefore aren't 'bluffcatchers' by definition

I mean, don't always call with a mid-range hand, but that's what people refer to as a 'bluffcatcher'

Got it. Makes sense. Thank you!

Imagine you're playing a game where the only cards in the deck are aces, kings and queens. Aces are the nuts, kings are mid-strength, queens are air.
Villain will bet with all aces to get value, and he'll bet some queens for balance and to make you fold some kings and all queens (he can get you off a better hand or a chop by bluffing with queens).
If villain is betting with all aces for value and some queens as bluffs, you need to call with some kings to stop villain making a profit with his bluffs (queens). Since your mid-strength hand beats villain's bluffs, but doesn't beat his value hands, you have a bluffcatcher.

Haha I like that Qs / Ks / As only world :P

The University of Alberta published a few interesting papers on it (it's alternatively known as Kuhn poker) if you're really interested.

Yes Im interested. Found some links already.
Kuhn poker: https://en.wikipedia.org/wiki/Kuhn_poker
UAlberta paper: http://poker.cs.ualberta.ca/publications/AAAI05.pdf