Grandparents are the parents of a person's father or mother – paternal or maternal.
As she is not a Mahram for him, marriage with her is permissible if all other conditions are fulfilled.
If her father and paternal are dead, she will be allowed to marry a believer who is compatible to her in Religion and morals.
You need to keep the respect of your grand parents in every possible way, provided that your marriage choice is according to Islamic teachings. The objection of your grand parents does not invalidate the marriage if there is no valid reason for their objection.
It is the etiquette of Islam that beds are not shared with someone of a different gender, whether they be related or not.
In this particular situation, it would be better to sleep in the same room, but on a different bed, or alternative options.
And Allah knows best.
Imam Ja'far al-Sadiq (as) was a descendent of Abu Bakr through his mother. After Abu Bakr died, his wife Asma married Imam Ali, and thus Abu Bakr's son, Muhammad,was raised by 'Ali ibn Abi Talib. He became a staunch 'Alawi supporter, openly protesting against the corruption of the third caliph 'Uthman and taking part in the siege against 'Uthman's palace. He became a general in the army of Imam Ali, and fought for him at the Battle of the Camel (against Talha, Zubayr and his own sister Aisha) and at Siffeen against Mu'awiya (who had been made governor of Syria by 'Umar ibn Khattab). 'Ali ibn Abi Talib made him governor of Egypt during his short caliphate, but Ibn Abi Bakr was killed by the army of Amr ibn al-As who operated under Mu'awiya's governorship.
There is no difference in this regard between any of the grandchildren. As long as a child lives his or her children or the children of other siblings would not inherit.
He had this right to gift any of his property to anyone he wanted and it doesn't matter that he himself inherited these properties and didn't acquire them through his own endeavors
No, since the siblings are the entitled to the inheritance according to Sharia law.