Learn Turkish: Sırf çalışmak istemiyor diye bahane mi arıyor? - Is he looking for an excuse just because he doesn't want to work?

You are right that diye originally comes from the verb demek (to say). However, in informal Turkish, it is very commonly used to mean "because" or "for the reason that." It acts almost like a quote of the underlying reason: "[Because of the fact that] he doesn't want to work."

What is the role of sırf in this sentence?

Sırf means purely, solely, or just. It pairs extremely naturally with diye to create the meaning "just because." Without it, the sentence would simply mean "Is he looking for an excuse because he doesn't want to work?"

Why do we use the fully conjugated verb istemiyor instead of a causal form with için?

That is the main advantage of diye! Unlike için, which requires you to turn the verb into a complex noun form (like istemediği için), diye lets you use a regular, fully conjugated verb right before it. It makes causal clauses much easier to build in everyday speech.

Why is the question particle mi placed after bahane instead of at the very end of the sentence?