Rabi’ al-Awwal 19, 1330
1) Yes, the Messenger of Allah (pbuh) had urged them to rush to participate in Usamah's campaign, ordering them to expedite, as you have mentioned, emphasizing his order till he told Usamah to invade Ubna in the morning, not allowing him to wait till the evening, telling him to go and emphasizing his order once more by telling him to rush.
But he, peace be upon him, according to all narrations, fell sick and started breathing very heavily, so much so that they started worrying about him and feeling too upset to leave him in such condition. They remained at Jurf waiting to know the condition of his health out of their own fear for his life and due to their attachment to him. They, therefore, are excused for having waited, and they should not be blamed.
As regarding their questioning the Prophet's appointment of Usamah after his death, in spite of what they remembered of his statements and his emphasis by word and by action, with which they were familiar, it was nothing more than their objection to his being too young, to his being a youth among middle-aged and old men.
The latter naturally find it very difficult to receive orders from the young, and they by nature feel resentful towards submitting to their judgment. Their hatred of his appointment was not an innovation but simply due to the human nature; so, consider that.
As regarding their demand after the demise of the Messenger to depose Usamah, this is justified by some scholars among those who expected the Siddiq [Abu Bakr] to agree with them. These persons thought that such deposition would, in their view, serve the public interest.
Yet, for the sake of fairness, I personally cannot rationalize their request to depose him after seeing how angry the Prophet (pbuh) was when they requested the same, and his going out, feverish, bandaged and wrapped in a blanket, to denounce such a notion in his sermon from the pulpit. They knew that such an incident was, indeed, a historical milestone; so, their real motive is not known except by Allah.
As regarding their determination to cancel the campaign, and their pressuring al-Siddiq to do so, in spite of seeing how much emphasis the Prophet had placed on its dispatch, his concern about expediting its departure, as well as his repeated statements to this effect, is but their own caution about the capital of Islam else it should be assaulted by the polytheists around it once vacated from a protecting force, while the army was far away from it, especially since hypocrisy surfaced as soon as the Prophet (pbuh) died, and the hopes of the Jews and Christians were revived, and a group among the Arabs renegated, while other groups refused to pay zakat.
The companions of the Prophet, therefore, spoke to our master al-Siddiq and requested him to forbid Usamah from leaving, but he refused and said: "It is better for me that birds snatch my flesh away rather than start my rule by overruling the command of the Messenger of Allah (pbuh)."
This is what our fellows have said regarding al-Siddiq. As regarding others, they are not to be blamed for trying to stop the campaign since their objective was nothing other than a genuine concern about the safety of the religion of Islam.
As regarding the question why Abu Bakr, ‘Umar, and others who were drafted in the regiment, lagged behind when Usamah proceeded, it was only to lay the firm foundations of the Islamic government, support the law of Muhammad (pbuh), and protect the caliphate, which was the only protector of both faith and the faithful.
2) As regarding what you have quoted of Shahristani's book Al-Milal wal Nihal, we have found it to be narrated without the name of its narrator. Both al-Halabi and Sayyid al-Dahlani, in their respective books of traditions, have said that in fact there was no such hadith at all in that meaning. If you, may Allah protect you, are able to narrate hadith from Sunnis supporting it, then lead me to it, Wassalam.