Given a finite dimensional algebra $A$ with finite global dimension such that there are only finitely many basic tilting modules. Then every selforthogonal indecomposable module $M$ (that is a module with $\mathrm{Ext}_A^i(M,M)=0$ for all $i \geq 1$) is a direct summand of a tilting module and thus there are only finitely many such indecomposable selforthogonal modules. See 3.9 in https://arxiv.org/abs/1803.10707.

Question 1: Is there an effective method to obtain every indecomposable selforthogonal module in a nice way? For example using the GAP-package QPA.

(A nice method would for example be an "Auslander-Reiten" theory for indecomposable selforthogonal modules in such algebras, where one can obtain every such module using certain exact sequences starting from just one such module.)

Question 2: Is there an example of an Auslander algebra with infinitely many selforthogonal indecomposable modules?