TL;DR: The answer to all your questions is No.
In his work "Ramakrishna Mission - In Search of a New Identity" (1986), Ram Swarup painstakingly sifted through historical records to refute claims of Ramakrishna embracing Islam and Christianity.
It is pertinent to point out that Ramakrishna's followers had taken upon themselves to reimage the Mission as "universal non-hindu" post the former's demise. But it gathered steam in 1980s when the Mission felt the need to identify itself as not a hindu religion in order to enjoy protection both from their staff as well as from the Marxist government in West Bengal. Institutions belonging to religious minorities are safe and their management secure from Government intervention, very unlike institutions run by Hindus which enjoy no such protection and which are subject to all kinds of interference from a Government.
They found intermediate success when High Court of West Bengal accepted their argument on being distinct from Hinduism -
Arguing for the “distinct” existence of the Mission, the affidavit says that not all its members are Hindus and, in fact, some of them are Muslims and Christians. The first fact proves that it is non-sectarian, the second that it is universal. This is the pattern which the afhdavit faithfully observes-when the inclusiveness of the Mission is to be shown, Islam and Christianity are mentioned; when its distinct character is to be shown, Hinduism is mentioned. The Mission is distinct from Hinduism in some respects and similar to Islam and Christianity in others. That makes it unique and universal —that is the line of argument.
The Mission also claims to be “unique” on the ground that its followers believe in the “universal brotherhood of all, irrespective of caste, creed, community, language and nationality.
However to to bolster their claim of a new identity they conjured Ramakrishna's image "as a practitioner of all religions"
As regards Ramakrishna’s “practice of Islam and Christianity” of which the Mission makes so much, it finds no mention in the Gospel, the earliest and most authentic account of Ramakrishna’s thoughts and experiences in his own words. In this work we find that though Ramakrishna reminisces often about his experiences and God-filled states, there is hardly a word about his so-called practice of Islam and Christianity. It first finds place in Swami Saradanandas biography, “Sri Ramakrishna: The Great Master’, a devout work alright but not “untarnished by the writer's mind’, an eminent quality of the Gospel in the words of Vivekananda. The author had met Ramakrishna in the last two years of the latter’s life and the work itself was written 25 years after when an incipient theology of the Mission had already emerged and when the Mission was learning to look at its old master in the light of its future work as it conceived it.
Also from Saradanandas' work we learn that in a life devoted to intense Sadhana extending over many years, the so-called practice of Islam and Christianity occupied no more than three days.
In November 1874, the practice of Christianity followed about the same course except that it involved not even this initial Sadhana. He had listened to some readings from the Bible (one wonders what portions) and he was moved. One day sitting in the parlour of a devotee, he saw a painting of the Madonna and the Child on the wall. Presently, Ramakrishna became ecstatic. The mood last for three days, at the end of which he saw a luminous figure appearing, entering into and merging with him. (The affidavit mentions this). This, Swami Saradananda calls the “Master’s vision of Sri Ish.”
Even if Saradananda's account, who met Ramakrishna only in his last 2 years and wrote his biography 25 years later, is accepted at face value , it in no way points to Christianity as an acceptable path. For an average Christian, image of "Ish" merging with Ramakrishna is undoubtedly an insult. Furthermore it is nothing unusual about Ramakrishna's visions of "Ish" from a Yogic viewpoint
When one meditates on the object (Karmasthana), it undergoes several
successive modifications. It gets internalized; it loses its
blemishes; it assumes a luminous form (jyotishmati); it assumes a
joyous form (visoka). All this is a normal process of yogic
modification and ingestion. The same thing happened to the “thoughts”
of Muhammad and Jesus when they passed through the cricible of
Ramakrishna’s mind. It need not give birth to an indiscriminate
theology like the one produced by the Mission that all prophets and
religions are equal and that they all say the same thing
