This question is drawn directly from the syllabus, hence, would require a comprehensive response. It basically outlines how the extent in which the author's judicious manipulation of language and textual forms simultaneously mirror and castigate prominent post-WII concerns.
I have not read Kazuo Ishiguro's An Artist of the Floating World, but I am familiar with Waiting for Godot.
These are just some ideas to get you started and by no means are the 'correct' answers. They're just my thoughts
Consider the way in which Beckett challenges aggressive political regimes within Waiting for Godot and how it constricts individuals. Many examples can be seen about this in the play, such as the title itself, or the motif of a tether or the ambiguous relationship between Pozzo and Lucky. All of this involve a fragile yet complex power play that render the main protagonists to remain in anticipation. This is reflective of the belief during the time when the world would be destroyed by the atomic bomb in events such as the Cuban Missile Crisis or the paralysing anxiety of "The Red Scare" where individuals had no choice but to 'wait' for the inevitable.
For the personal values, consider the permeating existential dilemmas as well as the absurdist claims prominent in the post-WII milieu. Many individuals, within the 'after the bomb' zeitgeist, were left disoriented in a world capable of annihilating itself due to ravaging effects of nuclear warfare. As a response to this, existentialism and absurdism became prominent way to rationalise the devastating effects of mechanised global warfare. Attempts at intellectual discourse, such as Vladimir's endeavours to think and Lucky's famous extended monologue, ultimately become useless in asserting their existence in a world disheartened by Cold War anxieties. Basically, there was an intensified requisitioning of the human condition and widespread abandonment of established values.
Hope this helps