Short answers, pulled from the story.
John Hicks presented the new mathematical framework at the Econometric Society in Oxford during September 1936. He originally called it the LL curve instead of LM before the name changed.
The downward-sloping IS curve shows how every level of real interest rate generates a certain level of investment and spending. The upward-sloping LM curve represents combinations of interest rates and income levels where money demand equals money supply.
David Romer published suggestions in 2000 replacing the traditional positively sloped LM curve with a horizontal MP curve because central banks started paying little attention to money supply when deciding on policy. Central banks generally changed strategies towards targeting inflation rather than money growth starting from the early 1990s.
Daron Acemoglu, David Laibson, and John A. List named their corresponding model combining IS-LM with changing price levels as an IS-LM-FE model in their 2018 textbook Macroeconomics. The original model assumed fixed price levels so it could not analyze inflation which became problematic with rising inflation levels in the late 1960s and 1970s.
Today the IS-LM model is largely absent from macroeconomic research but remains a backbone conceptual introductory tool in many undergraduate textbooks. Advanced economic courses generally accept the model as imperfect and skip its use in favor of more complex dynamic models.