Was the grandfather of Rasolullah, Abdul Mutalib, Muslim?
I couldn't find much about him, maybe I'm missing some narrations.
Followers of the Shia school of thought believe, that Abdul Mutalib, the grandfather of the Holy Prophet(peace be upon him and his holy progeny), was a Muslim in the sense that he believed in monotheism, as all direct ancestors of the Prophet did, back to the Prophet Ibrahim (peace be upon him), who was the champion of Monotheism.
Abdul Mutalib was the chief of Quraysh in Mecca at the time when Abraha and his army came to destroy the Kabaa, the incident which is recorded in Sura 105, Al-Feel. Abdul Mutalib came to the camp of Abraha and demanded his camels back which had been seized by Abraha's soldiers. He was astonished that the chief of Quraish did not ask for the safety of the Holy House.
In reply to Abraha's remarks Abdul Muttalib spoke a sentence, whose value and worth is still preserved. He said: "I am the owner of the camels. The House too has a Master who forestalls every intrusion upon it".
In the Tafsir of Ibn Katheer regarding the Sura you can find the following prayer being offered by Abdul Mutalib:
Abdul-Muttalib said, while hanging on to the ring of the Ka`bah's door, "There is no matter more important to any man right now than the defense of his livestock and property. So, O my Lord! Defend Your property. Their cross and their cunning will not be victorious over your cunning by the time morning comes.''
In the book "Perfection of Faith and Completion of Divine Favor" written by the highly respected Shia scholar of the 4th century a.H., Shaikh as-Sadooq, the following hadith can be found:
5 - Narrated to us Ahmad bin Muhammad as-Saigh that he said: Narrated to us Muhammad bin Ayyub from Salih bin Asbat from Ismail bin Muhammad; and Ali bin Abdullah from Rabi bin Muhammad Musalli from Saad bin Tareef from Asbagh bin Nubatah that he said: I heard Amirul Momineen (a.s.) say: “By Allah, my father, my grandfather Abdul Muttalib, Hashim and Abde Manaf never worshipped idols. He was asked: Then what did they worship? He replied: They used to face the Kaaba and pray according to the religion of Ibrahim (a.s.) and they followed only that faith.” [….]
The given examples are only a few out of many, to provide evidence that Abdul Mutalib was a Muslim.
Rabiah bin Saif Al-Mu'afiri narrated from Abu 'Abdur-Rahman Al-Hubuli, from 'Abdullah bin 'Amr, who said: "while we were traveling with the Messenger of Allah, he saw a woman, and did not think that he knew her. When she was halfway to him, he stopped until she reached him, and it was Fatimah, the daughter of the Messenger of Allah. He said to her: 'What brought you out of your house, O Fatimah?' She said: 'I came to the people of this deceased one to pray for mercy for them, and to offer my condolences to them.' He said: 'Perhaps you went with them to Al-Kuda?" She said: 'Allah forbid that I should go there. I heard what you said about that.' He said: If you had gone there with them, you would never have seen Paradise until the grandfather of your father saw it."'
An-Nisai - Hadith is Daif (weak) by Albani and Arnaodi
Majority of scholars said that the hadith doesn't mean Abd Mutalib is in Hell. But it means at the day that Abdul Mutalib sees the fire, then Fatima would see the paradise(She will be delayed from seeing the paradise)
and some Scholars said he is from أهل الفترة (Ahlu Al-Fatrah - wikipedia)
While Ibn Kathir in His book اليداية والنهاية stated that the hadith is clear and he is considered in kafir.
Shia believe he was a muslim.
It is not for us to judge whether a person is a Muslim or not, that is down to the decree of Allah(swt). However, Prophet Muhammad's(pbuh) father died before Prophet Muhammad(pbuh) was born and Abdul-Mutallib died when the Prophet Muhammad(pbuh) was 8 (I think). The revelation occured when the Prophet Muhammad(pbuh) was at 40, so Allahu A'alam.
There are some Hadiths which can give indication to what happened however, it is not for us to judge whether a person a Muslim, only if through the will of Allah(swt).
Here is some further information if you want to learn more: http://islamqa.info/en/43045
No he was not, he died at the religion of his ancestors and the Prophet asked him many times to testify that no one but Allah and that he is the messenger of Allah, but he didn't make it, one of the major reasons was his companionship that didn't believe the prophet
Abu Taleb went to Hell and he is the least one to be tortured as the prophet said, his punishment is to stand over a cinder (Jamrah) from hell till his body boils from inside.
At that time Arabs were divided into many religions such as Christianity, Judaism, Polytheism (idols), some Assyrian religions etc. And there were Hanifs, the ones who believe in One God (Abraham(puh)'s God), but they didn't know how to pray, how to worship.
I heard that Mohammad(puh)'s parents and also him were Hanifs. And we know that some of his uncles were polytheist. Maybe, his grandfather was also a Hanif and taught his belief to his son Abdullah(ra).