One report concludes that many schools do not have, nor are they likely to have<---we repeat "they", and we can't omit "they".
why for this sentence, we need to omit "it"?
Repeating pronouns in parallel structures is often an error in SC problems. For example, the sentence "Miho plays football and she goes skiing." would be incorrect as we don't need the pronoun "she". Better to write "Miho plays football and goes skiing."
However, in more complicated sentences, we might need to adjust this rule. If I wanted to say something with a negative, such as "On Saturdays my friends don't play football and go skiing." I might get mixed up: do I mean that they go skiing or not? I would encourage you to think of the construction 'nor do they...' as a solution to this. If I write "On Saturdays my friends don't play football, nor do they go skiing." then it's clear that they don't do either. If I write "On Saturdays my friends don't play football, but they go skiing." then it's clear that the 'don't' only applies to 'football' and that my friends do, indeed, go skiing.
Note that in the example that you cited there's no option that omits the 'they'. It looks like GMAT considers the issue of leaving out the 'they' to be too subjective to be worth testing in this case.
As for the classical guitar example, I don't think that the potential inclusion of 'it' is a pressing issue. The two problems that I'd encourage you to pay attention to are: combining passive and active in a parallel construction (incorrect) and the use of the verb 'perform' (the sentence states that
classical guitar was performed; musical instruments can be played, not performed).