Some might think that this is a chemistry question, and indeed most of the work is done in chemistry departments, but that isn't because its not biology.
As far as evolutionary theory, there is a well-established definition of life as self-replicating systems and very little else. Richard Dawkins' theory of the Replicator is not always completely accepted (the link is to Stephen Gould's essay, who was usually in the opposition to Dawkins until he passed away). Nonetheless, its logic is hard to completely dismiss: Once and only once chemical systems can self replicate then evolution happens - selection, variation and replication. Dawkins thought springs from the pretty justifiable position that DNA is the center of all inheritance and variation in living things. I'm not going to get into the arguments for and against but suffice to say that the replicator model might not be entirely true, but its not entirely wrong.
As far as the fourth step you mention, there are theories which are very credible but its reasonable to say that we are short on details... they may not satisfy and they certainly have not duplicated step 4... The most detailed and credible theory is the RNA World Hypothesis. At some stage, RNA polymers were able to self-replicate, pretty much by themselves it seems.
The evidence for RNA world is compelling but its more molecular archaeology than a series of coordinate events as we see it. The ribosome and other RNA genes show that RNA could be fundamental genes. In particular the ribosome consists of RNA whose structure are supported by protein, but RNA does all the chemical work.
Consider the odds. The prebiotic soup may have existed for the better part of a billion years and covered all or a good part of Earth during much of that time. As such, its exceedingly unlikely that we will be able to reproduce self replication of RNA in the lab. Lucky and intelligent guesses may produce an environment that is just barely pre-biotic and produce a replicator, but even that seems quite unlikely. Almost all this work tries to show that compounds and processes that come close to life are possible in pre-biotic Earth.