The statements 1, 2, 3, 4 in the above quote (my numbering) are each false. Note that the poster has not provided any citations in support of any of these statements.
Here is the truth relating to each of these statements. The source of my information is: The Italian Code of Criminal Procedure: Critical essays and English translation, ed. Mitja Gialuz, Luca Luparia, and Federica Scarpa; Wolters Kluwer Italia (c) 2014.
1. Code of Criminal Procedure (CPP) Article 620 is the Italian procedural law which governs the annulment of an appealed case without referral by the Supreme Court of Cassation (CSC). There are ten sub-paragraphs, 1A through 1L, each describing a situation or status where the CSC may annul a case that has been appealed to it without referral. The tenth, 1L, is very broad; it states:
Thus, if the CSC panel reviewing an appeal believes that the judgment of the lower court should be annulled, it has the legal authority to do so. If it believes that referral after annulment is unnecessary, it need not refer the case. Finally, the CSC has the authority to determine the sentence - which means it may follow or invoke any of the CPP Articles 529 (Judgment of non-prosecution), 530 (Judgment of acquittal), 531 (Declaration of extinguishment of the offence), 533 (Conviction of the accused person), or any of the other articles of sentencing, such as those relating to civil actions.
2. This statement is obviously false. There is in fact no authority in Italy, with the possible exception of the Supreme Constitutional Court, which could by law judge the legality of a CSC decision. If a CSC decision were to allegedly violate the Convention rights of a person, for example by allegedly wrongfully convicting as a result of a violation of ECHR case-law, that person can lodge a claim against Italy with the ECHR. That is what Amanda Knox has done with respect to her final conviction for calunnia against Patrick Lumumba. According to judgment No. 113/2011 of the Italian Supreme Constitutional Court, a revision trial may be requested in order to comply with a final decision from the ECHR. Final judgments of the CSC may not be appealed, and a retrial after a final acquittal by the CSC (which is what the Marasca panel has issued for Knox and Sollecito) would be a violation of the prohibition against double jeopardy.
3. The situation regarding the CSC invoking CPP Art. 530 was explained in (1). The CSC has the authority by CPP Art. 620 para. 1L to invoke this sentence. The findings of the lower courts have been annulled and are not at issue, although no doubt the CSC will make some mention of them in its Motivation Report.
4. The Marasca panel reviewed the judgment of the Nencini court in accordance with appeals, as provided for in CPP Article 606. While the Nencini court was obligated to follow the CSC interpretation of law, in accordance with CPP Article 627 para. 3. There was no obligation for the Nencini referral court to follow any interpretation of fact suggested by the Chieffi CSC panel. The CSC may not impose any interpretation of law that violates the explicit wording of the CPP, the Italian Constitution, or the intent of the Convention and ECHR case-law. Thus, the CSC is free understand the appeals in light of, for example: CPP Art. 606 para. 1e, the grounds of a judgment are lacking, contradictory, or manifestly illogical; and CPP Art. 606 para. 1b, failure to comply with or misapplication of criminal law or other legal rules which must be considered in the application of criminal law.
CPP Art. 606 para. 1e allows the CSC to evaluate the logic of how the evidence was evaluated by the lower court, among other things. CPP Art. 606 para. 1b allows the CSC to evaluate the conformance of the lower court procedures and legal reasoning to the CPP, the Italian Constitution, and the ECHR case-law.