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.
Both fasting on Mondays and Thursdays and fasting the 13th, 14th, and 15th of every lunar month are desirable, and the 13th, 14th, and 15th may coincide with Monday or Thursday as it is known. However, we have not come across any statement of the scholars about which one is more excellent than the other. It is only Allaah Who knows their reward.
However, the Sunnah stresses the importance of fasting on Mondays and Thursdays more than fasting on the 13th, 14th, and 15th of each month. On Mondays and Thursdays the doors of Paradise open and one’s deeds are presented to Allaah, and the Muslims are forgiven except those between whom there is enmity, and the Prophet used to fast these days. Moreover, it was on Monday that the Prophet was born and it was on Monday that he received the first revelation, and this excellence is not mentioned about the 13th, 14th, and 15th as far as we know.
Abu Hurayrah narrated that the Prophet used to fast on Mondays and Thursdays and he was asked: ''O Prophet of Allaah, why do you fast on Mondays and Thursdays?, and he replied: ''On Mondays and Thursdays, Allaah forgives to every Muslim except for two persons who are deserting each other, and Allaah would say to the angels, “leave them until they reconcile.” [Ibn Maajah]
This Hadeeth was narrated with a different wording by Imaam Muslim : “The doors of Paradise open on Mondays and Thursdays; and every servant who does not associate anything with Allaah will be forgiven, except a man who has enmity and disputes with his Muslim brother, in which case, Allaah would say: "Put both of them off until they are reconciled." [Muslim]
Besides, ‘Aa’ishah narrated that the Prophet used to fast on Mondays and Thursdays.” [Ahmad, Ibn Maajah, At-Tirmithi, Abu Daawood, An-Nasaa’i] Moreover, Usaamah said: “I saw the Prophet fasting on Mondays and Thursdays, so I asked him about it and he said: ''The deeds are presented (to Allaah) on Mondays and Thursdays, so I like that my deeds are lifted while I am fasting.” [An-Nasaa’i and Abu Daawood]
Also, Qutaadah narrated that the Prophet was asked about him fasting on Mondays and he said: ''It was the day on which I was born, and the day on which I was commissioned with prophethood, or the day on which the revelation was sent to me.” It is for this reason that Shaykh ‘Uthaymeen said: “The fasting of Monday is more confirmed than on Thursday.”
As regards the excellence reported about the fasting on the 13th, 14th, and 15th of each month that it is like fasting for the whole year because a reward is multiplied tenfold, then this reward and more than it could be achieved by fasting on Mondays and Thursdays of every week.
As regards your statement “can one take action on what he or she is not clearly certain about?” then this differs according to the matter that he/she wants to undertake. Some matters are in principle lawful and some matters are in principle forbidden. In general, the jurists stated that it is not permissible for a Mukallaf (a man/woman who is competent for religious assignments) to undertake a matter unless he/she knows the ruling of Allaah on it, even by asking about it.
Allaah Knows best.