Are these correct?
1: They made a choice WHAT to wear
2: They made a choice WHETHER to go to Italy or the UK.
Or should we write "They made a choice ABOUT what to wear" and "they made a choice ABOUT whether to go to Italy or the UK".
Thank you
They made a choice of what to wear.
See Ngram. "a choice of what ..." is more common than "a choice about what", and much more common than "a choice what". For "whether", all of these options are closer in frequency.
WHAT
They [made a choice] // [what to wear]. I would question whether this is correct although in spoken English it would be ok. Subject + verb + [interrogative + to-infinitive] is the usual pattern. The phrase "what to wear" acts like the object. In this case you would use "to choose" rather than "to make a choice": "They chose what to wear."
Other examples:
They [made a choice about] // [what to wear]. This is better. The [what to wear] construction is like a noun phrase
WHETHER
They [made] [a choice] // [whether] [to go] [to Italy] // [or] [to the UK]. This is correct. This sentence answers the question: "Did they make a choice?" "Whether"/"or" are two conjunctions expressing alternatives similiar to "either/or", "both/and". Compare:
They made a choice about whether to go... answers the question ABOUT WHAT did they make a choice? It's also correct. The answer is "whether to go to Italy or the UK". The whole clause introduced by "whether" acts like a noun phrase. Compare: