Hey madzienka,
Looking over the crash report it looks like the system in question is running an AMD phenom II 1100t. This CPU is below the minimum requirements of an AMD FX 4350.
As such we don’t have much in the way of support to ensure this CPU will always work with the game. Now its performance matches that of the FX 4350 but its missing some instruction sets currently required for the game. Now it is possible your issue is related to the intel equivalent where older intel CPUs that are fine performance wise are missing a set of AVX capabilities that the game client is currently requesting. This in itself is not intended a a fix is in the works for that particular issue but I cannot say whether it will solve your specific issue since that one seems focused more on the AVX specific issue and I do not know of that is the sole cause of the troubles you are seeing. I recommend following that thread for updates and see if that solves the issue for you. However do keep in mind that this does not mean the phenom II is supported so you may continue to encounter issues once that fix goes live. Ultimately the recommendation would be to upgrade/replace the system regardless of whether the AVX fix solves your current troubles.
Wojcza it looks like you are running an i7-870, also below the minimum requirements for d2r which would be an i3-3250. Again performance isn’t the issue it is the missing instruction sets. I am more confident your current issue would be fixed when the devs resolve the AVX issue however again, that does not make the CPU officially supported so you may see other unrelated issues now or in the future.
For both of you I recommend following the AVX thread updates for more information as we get it.