Imperfection in ‘Umrah’s (lesser pilgrimage’s) recommended acts does not invalidate it

Question

After Tawaaf (circumambulation of the Ka’bah), I performed two Rak‘ahs (units of prayer) at the Standing Place of Ibraaheem (Abraham), may Allah exalt his mention, but with my right shoulder uncovered. Is my ‘Umrah valid? Also, at the first round of Sa`y (walking between Mounts As-Safa and Al-Marwah) while on As-Safa mount, I said, “Laa ilaaha illa Allah (there is no god but Allah)” once, but on the other rounds I repeated it thrice. Is my ‘Umrah valid?
Fatwa
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah, and that Muhammad  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) is His Slave and Messenger.
Your ‘Umrah is valid and there is nothing (further) due from yourself. What you mentioned in the question has no effect on the validity of the ‘Umrah.
Regarding the first issue, you should know that covering the shoulders in prayer is recommended according to the majority of scholars. It is obligatory only according to one of the two views of the Hanbali scholars who were also of the view that it is obligatory to cover only one of the two shoulders. Your left shoulder was indeed covered. Also, they were of the view that covering the shoulders is due in the obligatory prayer, not the voluntary prayer. According to the majority of scholars, the two Rak‘ahs of Tawaaf are an act of Sunnah (recommendation).
Consequently, the two Rak‘ahs of Tawaaf that you performed while one of your shoulders was uncovered are valid according to the views of the four Imaams.
Even if we were to suppose that the two Rak‘ahs of Tawaaf that you performed are invalid, or even if you did not pray them at all, your ‘Umrah is still valid and there is nothing due upon you. According to the preponderant opinion, the two Rak‘ahs of Tawaaf are an act of Sunnah, and this is the view of the majority of scholars.
Ibn Qudaamah  may  Allah  have  mercy  upon  him said,
The two Rak‘ahs of Tawaaf are a confirmed act of Sunnah but not obligatory. This is also Maalik's view. Ash-Shaafi‘i has two views: one of them is that the two Rak‘ahs are obligatory because they are affiliated to Tawaaf and therefore they are obligatory like Sa‘y. As evidence of our view, we have the Hadeeth in which the Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) said: "Allah made five prayers (per day) obligatory on the servant. Whoever perfectly performs them, for him will be a promise from Allah to enter Paradise." The two Rak‘ahs of Tawaaf are not included. Likewise, when the Bedouin asked the Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) about the obligatory prayers, he mentioned the five prayers. Then the Bedouin asked again if there were other obligatory prayers and the Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) answered: "No, unless you perform voluntary prayers."
As for the second issue which is not performing some of the prescribed mentionings of Allah on Mount As-Safa, there is no harm at all in this. According to the Sharee‘ah prescriptions, the referred to mentioning is to be said thrice on both As-Safa and Al-Marwah in all rounds. This is in compliance with what the Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allah exalt his mention ) did as stated in the long Hadeeth narrated on the authority of Jaabir, may Allah be pleased with him, describing the manner of Hajj. If a pilgrim does not ascend the mountain in the first place, there is nothing due upon him, so failing to say this mentioning is of no consequence with greater reason.
Ibn Qudaamah  may  Allah  have  mercy  upon  him said,
If he (the pilgrim) did not ascend the mountain of As-Safa, there is nothing due on him. Al-Qaadhi said, “Rather, he is required to go through most of the distance between As-Safa and Al-Marwah."
We do not know of any scholar who says that it is obligatory to say this mentioning on As-Safa or Al-Marwah.
We alert you to the fact that the Sunnah is to say this mentioning when one ascends As-Safa or Al-Marwah, and not during the Sa‘y, as your question implies.    
And Allah knows best.

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