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.