Suppose $A$ is commutative local (necessarily artinian) with the only simple $k\neq A$  then $\psi_k=1$, so your statement 1 will say that $Ext^1_A(M,M)=0$ implies $M$ is free.  I stated it as a conjecture for complete intersections [here](https://link.springer.com/chapter/10.1007%2F978-1-4614-5292-8_10) (conjecture 9.1.3). Technically, it was stated as $Ext^1_A(M,N)=0$ implies $Ext^i_A(M,N)=0$ for all $i>0$, but when $M=N$ the latter condition is equivalent to $M$ being free. 

One could also ask if $Ext^1_A(M,M)=0$ implies $M$ is free, still assuming that $A$ is Gorenstein. It was stated as a question (9.1.4) in the same survey. 

As far as I know, both are open even for complete intersections unless $A$ is a hypersurface (which will be representation finite anyway).