Trading seems completely fine with the spirit of ARAM, as it has no effect on teamcomps and therefore no effect on balance. Rerolls are theoretically fine, as they help mitigate bad luck with initial teamcomp rolls.
I agree that limited champ pools are not fine though, as some players (i.e. ARAM-optimized accounts) take advantage of the limitations to unfairly bias their chances of a strong pick. On the other hand, I'd argue that it's more of a game health issue than a game balance issue. ARAM is lacking in Riot support, so champion power disparity is natural consequence. Running into a strong champ or two is fairly expected. Running into the same strong champs for multiple matches in a row makes that power gap much more evident and frustrating.