a) Surahs Al-Ikhlaas, Al-Falaq and An-Naas are to be recited 3 times in morning and in evening (Asr or Maghrib time), before sleeping, when sick, etc. But which of the methods below is the allowed way of reciting? Or are both allowed? Or does it depend upon the time and situation? (i) Surah Al-Ikhlaas, then Surah Al-Falaq, then Surah An-Naas. Then again Surah Al-Ikhlaas, then Surah Al-Falaq, then Surah An-Naas. Then again Surah Al-Ikhlaas, then Surah Al-Falaq, then Surah An-Naas (i.e all together 3 times). (ii) Surah Al-Ikhlaas 3 times, then Surah Al-Falaq 3 times , then Surah An-Naas 3 times (i.e 3 times individually each) Assumption: Bismillah is recited every time a surah is recited. b) Is it true that dhulm (oppression/injustice) can also be classified into 3 types: (i) Unforgivable – Shirk (polytheism).(ii) that which Allaah does not leave – the dhulm between humans, huqooq ul 'ibaad (iii) that which probably might be forgiven – what is between a person and Allaah (I am referring to Q #87847, Sins that Allah will not forgive; and certain hadiths probably in Abu Dawood at-Tayaalisi in his Musnad; Abu Nu'aim in al-Hilyah; Silsilat al-Ahaadeeth as-Saheehah, vol. 3, pp. 560-561; Shaykh Jamaaluddeen Zarabozo: Commentary on the Forty Hadeeth of Imaam an-Nawawi vol. 2, pp.759-762 )

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.

It has been authentically reported that the Prophet, sallallaahu ʻalayhi wa sallam, said to one of his Companions, "Recite Al-Ikhlaas and Al-Muʻawwithatayn (Al-Falaq and An-Naas) thrice in the morning and evening; they will suffice you against everything." [Abu Daawood and At-Tirmithi]

Reciting these chapters thrice can be done in the two manners that you mentioned in the question; one may recite Al-Ikhlaas and then Al-Muʻawwitthatayn and repeat them thrice or recite each chapter thrice in turn.

As for your question whether the person should recite the Basmalah before each chapter in this case, you should know that it is recommended to seek refuge with Allaah from the Devil and recite Basmalah before reciting any chapter of the Quran. The Kuwaiti Encyclopedia of Fiqh reads:

“According to the scholarly consensus, it is recommended to seek refuge with Allaah from the Devil before reciting the Quran outside of prayer ... It is also recommended to recite the Basmalah before reciting all chapters of the Quran, except for At-Tawbah (chapter 9) ... Ibn Muflih said, ‘If he recites (Quran) outside of prayer, then he may recite the Basmalah aloud or silently ...’” [Briefly excerpted]

As for the classification of sins mentioned in the question, some hadiths made reference to this point. For instance, Anas narrated that the Prophet, sallallaahu ʻalayhi wa sallam, said:

“There are three categories of thulm (oppression/injustice): the one that Allaah never allows to go unpunished, the one that is forgiven, and another that is not forgiven. Thulm that is not forgiven is shirk; thulm that is forgiven is that which is between the individual and his Lord (i.e. falling short in fulfilling the due rights of Allaah over the slave); and thulm that is never left unpunished is that which the slaves perpetrate against one another – until the wronged shall be compensated with their right of retaliation against his transgressors.” [Abu Daawood At-Tayaalisi and Al-Bazzaar]

Moreover, ʻAa'ishah narrated that the Prophet, sallallaahu ʻalayhi wa sallam, said:

“The records with Allaah are three: a record that Allaah does not mind at all, a record of which Allaah will leave nothing out, and a record that Allaah will not forgive. As for the record that Allaah will not forgive, it is shirk; Allaah, The Exalted, says (what means) {Indeed, he who associates others with Allaah – Allaah has forbidden him Paradise, and his refuge is the Fire.} [Quran 5:72] And as for the record that Allaah does not mind at all, it is the wrongs that the slave does to his own self, which are between him and his Lord – in terms of a fast that he left off or a prayer that he left off, for Allaah will indeed forgive that and pardon (him), if Allaah wills. As for the record from which Allaah will leave nothing out, it is the transgression committed against one another: al-qisaas (due retaliation against the transgressor), with the utmost certainty (that it will occur).” [Ahmad in Al-Musnad; Al-Haakim in Al-Mustadrak]

The term 'records' refers to the three categories of transgression written therein.

Allaah knows best.