Relative stability of carboxylic acid derivatives This picture depicts the relative stability associated with resonance structure.

My questions are: 

1.1. Teacher says anhydride is less stable because of two reasons above.
but it seems there's no reason the resonance of anhydride would be less likely compared to acetate.
1.2. and about reason #2, the actual structure is the hybrid of these resonances so it's hard to agree with this reason.


Why won't Cl give its e- pair to adjacent carbon for resonance structure. 


Someone says it's about electronegativity but it contradicts with resonance associated with oxygen. And someone says it's about the high energy orbital of Cl (n=3) but I can imagine a acetyl fluoride and this logic doesn't solve this problem anymore.
Firstly "stabilised" is very ambiguous. "Stable" is always defined with respect to something. The proper phrasing here should probably be stable towards nucleophilic attack.

For the anhydride - yes the actual structure is a hybrid. That just means that both C=O have to "share" the central oxygen's lone pair - in a sense each of them get half resonance each - which means that both C=O's are not very stabilised.

I don't buy the "less likely" explanation. Your teacher is trying to say that there's a "50% chance" that at any one point in time a particular C=O is stabilised, but resonance isn't something that you flip a coin and decide which way it goes.

For the acyl chloride, it is really to do with the leaving group ability of Cl-. See this question for a discussion: Do acyl fluorides exhibit resonance donation or inductive withdrawal?

Essentially the idea is that since $\ce{Cl-}$ is a better leaving group than $\ce{OMe-}$, for the acyl chloride (X = Cl), resonance form 2 contributes more to the actual structure than it does in the ester (X = OR):



As you can see, resonance form 2 makes the C=O more susceptible to nucleophilic attack because of the positive charge associated with the carbonyl group. Therefore, any substituent X that favours resonance form 2 will make the carbonyl group less stable towards nucleophiles.