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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm on a pilgrim to optionally fast on Monday and Thursday unless these days correspond with the day of 'Arafah, 'Eed Day and the three days that follow 'Eed day.
The Hanbali and Maaliki schools are of the view that it is disliked for a pilgrim to fast the day of 'Arafah, rather it is desirable for him to break the fast. At-Tirmithi said: 'The view of the majority of scholars is that it is desirable for a pilgrim to break the fast so that he would preserve his strength for supplicating.' However, the Shaafi'ee school considers that it is more proper for him not to fast. The evidence for their view is the narration reported by Imaam Al-Bukhari and Muslim that the companions differed about whether the Prophet was fasting on 'Arafah or not, so Um Al-Fadhal, sent to the Prophet a goblet of milk while he was on his camel in 'Arafah, and he drank it. Therefore, the Prophet did not fast on 'Arafah day.
Ibn 'Umar was asked about fasting [for a pilgrim] on the day of 'Arafah and he replied: "I performed Hajj with the Prophet and he did not fast, and I performed Hajj with Abu Bakr and he did not fast, and I performed Hajj with 'Umar and he did not fast, and I performed Hajj with 'Uthmaan and he did not fast, so I am not going to fast on this day but I do not prohibit you from fasting it." [Ahmad]. So, if a pilgrim fasts on this day, there is no harm on him and he is not sinful.
As regards 'Eed Day, it is forbidden to fast it, whether for a pilgrim or non-pilgrims. The evidence for this is that Abu Sa'eed Al-Khudri narrated that the Prophet forbade people from fasting two days: the day of 'Eed Al-Fitr and 'Eed Al-Adh-Haa. [Al-Bukhari and Muslim] Furthermore, Imaam An-Nawawi said: 'The scholars agreed in a consensus that it is forbidden to fast on the days of 'Eed ['Eed Al-Fitr and 'Eed Al-Adh-Haa] for the existence of the above narrations, and if a person fasts these days, his fasting is not accepted.'
It is also not permissible to fast the days that follow 'Eed Al-Adh-Haa, i.e. 11th, 12th and 13th of Thul-Hijjah with the exception of a pilgrim who performs Hajj Tamattu' and cannot afford to offer a sacrifice to slaughter [in Makkah]. 'Aa'ishah and Ibn 'Umar narrated that ''the Prophet did not give permission for a pilgrim to fast except the one who could not afford a sacrifice to slaughter [in Makkah]". [Al-Bukhari] Thus, it is forbidden to fast on 'Eed Al-Adh-Haa day and on 11th, 12th and 13th of Thul-Hijjah, and it is desirable for a pilgrim to break fast on 'Arafah. As regards other days, like fasting the first eight days of Thul-Hijjah, then it is a Sunnah to fast these days, but the Shaafi'ee school are of the view that it is a Sunnah even for a pilgrim to fast on these days.
Concerning the forgiveness of sins apart from repenting and making ablution, it is to perform good deeds as much as possible, as Allaah says (which means): {Verily, the good deeds remove the evil deeds (i.e. small sins). That is a reminder (an advice) for the mindful (those who accept advice)}[Quran 11:114]. Finally, it should be noted that the most dangerous thing that the devil involves a person in is to make him despair from Allaah's Mercy and His Forgiveness. Allaah says (which means): {Say: 'O My slaves who have transgressed against themselves (by committing evil deeds and sins! Despair not of the Mercy of Allaah; verily, Allaah forgives all sins. Truly, He is Oft-Forgiving, Most Merciful'.}[Quran 39:53]. In another verse Allaah says when speaking about Ibraaheem [Abraham] (which means): {Ibraaheem (Abraham) said: "And who despairs of the Mercy of his Lord except those who are astray?"}[Quran 15:56]. So a person should think good of his Lord and should repent. Moreover, the Prophet said: "Hajj expiates the previous sins." [Muslim]
Allaah knows best.