Good overviews on $\phi^{4}$-field theory?

This reference is a bit older, but it should be a good starting point for items 2 and 3: $\phi^4$ field theory in dimension 4: a modern introduction to its unsolved problems.

Concerning item 1, you might find it instructive to motivate the $\phi^4$ field theory from the perspective of its limitation: when does it apply and when are higher order terms needed? For that perspective I would recommend Higher-order field theories: $\phi^6$, $\phi^8$ and beyond.

This last reference is a chapter from a recent book, A Dynamical Perspective on the $\phi^4$ Model (2019) which has an interesting introductory chapter on the history of the $\phi^4$ model, as well as overviews of more specialized topics.

In terms of physical motivation of $\phi^4$, if I remember rightly the references in the introduction to this paper might have some pointers.

• Dashen R and Neuberger H 1983 How to get an Upper Bound on the Higgs Mass, Physical Review Letters 50, 24

Reference [7] of that article points to rigorous proofs of results which almost show the triviality of $\phi^4$ in four dimensions.