You are wrong about inability to reproduce. At least one recent replication was done in Poland (2015) by a respected academic team incl. professor Dolinski. The main result was consistent with what Milgram observed: most people did what they were told.
My understanding is that there have also been semi-recent replications done in France, Iran, and a partial replication conducted at Santa Clara university. All found the same basic pattern as the original study.
Yes. There have been dozens of replication efforts -- none of them exact replications. The closest and most careful one that I know about is the one done by Jerry Burger at Santa Clara University: "Replicating Milgram: Would People Still Obey Today?" It's at https://www.apa.org/pubs/journals/releases/amp-64-1-1.pdf.
I wonder the impact of how widespread the knowledge of the original Milgram experiments is. If the subjects figure that the pain is fake because they've heard about this experiment before they might be more willing to administer the shock.
https://www.sciencedaily.com/releases/2017/03/170314081558.h...