traceroute any website the first IP after the ISP gateway is a private range one (10.1.74.xx).
Is it normal? Can it cause any problems (problems for Postfix delivering messages for example)?
It's not abnormal or normal - all of the hops in between your host and the final destination are invisible to the actual packets. All they care about is end to end reachability. It sounds like you're having another problem, perhaps? But to answer your question, no, in and of itself, it doesn't cause any problems.