This answer is from a Sunni point of view. Neither narration has any origin, and are not considered to be authentic hadiths.
The first narration was documented by 'Abdur-Rahman ibn 'Abdul-Salam as-Safuri in Nuzhat al-Majālis (Arabic: نزهة المجالس ومنتخب النفائس), Vol. 1, pp. 210:
حضر مجوسي عند إبراهيم عليه السلام فجاءه بطعام ثم قال: "هل لك في الإسلام رغبة؟" فترك الأكل وانصرف فأوحى الله إليه: "يا إبراهيم أنا أرزقه على كفره منذ أربعين سنة وأنت تريد أن ترده عن دينه بأكلة واحدة" فخرج في طلبه فوجده فأخبره بذلك فأسلم ورجع معه إلى طعامه
— NOTE: My own translation, so treat with care:]
A man from the Majus visited Ibrahim ﷺ, and he brought the visitor some food. Then Ibrahim ﷺ asked the man: "Do you have a desire in Islam?" The visitor left the food and went away. Allah revealed to him: "O Ibrahim, I have been providing for him with his disbelief for forty years, and you want to turn him away from his religion with one meal?" Ibrahim ﷺ went out in his pursuit and told him so. The visitor became a Muslim and returned with Ibrahim ﷺ to his meal.
The narration is the closest I could find to what you quoted (there are minor differences) in a book. It does not have any chain associated with it, and it is not considered authentic.
The second narration you are referring to is:
ما يروى أن الخليل لما ألقي في المنجنيق قال له جبريل: سل، قال: حسبي من سؤالي علمه بحالي
— NOTE: My own translation, so treat with care:
It is narrated that the Hebronite [Ibrahim] when he was thrown onto the catapult, Jibril said to him: "Ask." He said: "Enough is His knowledge of my situation to suffice me from asking."
This narration has no origin in Islam.
In Majmū' al-Fatāwa, Vol. 8, pp. 519-523, Ibn Taymiyyah mentioned that this attribution is false and against the teachings of Allah (see Qur'an 2:201). He then added that what 'Abdullah ibn Abbas said is that Ibrahim ﷺ supplicated "Sufficient for me is Allah, and He is the best Disposer of affairs."
You may refer to Qur'an 3:173 for a better understanding of this supplication (very common among Muslims).As to what Ibn Taymiyyah meant by the words of the narration going against the teachings of Islam, Allah tells us in the Qur'an that was it not for our supplication, Allah would not care for us:
قُلْ مَا يَعْبَأُ بِكُمْ رَبِّي لَوْلَا دُعَاؤُكُمْ ۖ فَقَدْ كَذَّبْتُمْ فَسَوْفَ يَكُونُ لِزَامًا
Say, "What would my Lord care for you if not for your supplication?" For you [disbelievers] have denied, so your denial is going to be adherent.
— Surat Al-Furqan 25:77
It is part of the Islamic creed that one supplicates all the time:
وَقَالَ رَبُّكُمُ ادْعُونِي أَسْتَجِبْ لَكُمْ ۚ إِنَّ الَّذِينَ يَسْتَكْبِرُونَ عَنْ عِبَادَتِي سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِينَ
And your Lord says, "Call upon Me; I will respond to you." Indeed, those who disdain My worship will enter Hell [rendered] contemptible.
— Surat Ghafir 40:60
The Prophet ﷺ said the value of supplication is central to the worship of Allah in this authentic narration:
عن النعمان بن بشير، قال سمعت النبي صلى الله عليه وسلم يقول: الدعاء هو العبادة. ثم قرأ: وقَالَ رَبُّكُمُ ادْعُونِي أَسْتَجِبْ لَكُمْ إِنَّ الَّذِينَ يَسْتَكْبِرُونَ عَنْ عِبَادَتِي سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِينَ
Narrated An-Nu'man bin Bashir that the Prophet (ﷺ) said: "Supplication is the worship." Then he recited: "And your Lord said: 'Call upon Me, I will answer you. Verily, those who scorn my My worship, they will surely enter Hell in humiliation" (َQur'an 40:60).
— Jami at-Tirmidhiو Book 47, Hadith 3555