Did the Prophet (blessings and peace of Allah be upon him) see an army of Allah, may He be exalted, in the fourth heaven that had neither a beginning nor an end?

As for the issue of the number of the angels, their number is huge. This is proven in the hadith of the Mi‘raj (Prophet’s ascent to heaven), which was narrated by Malik ibn Sa‘sa‘ah (may Allah be pleased with him), who said: The Prophet (blessings and peace of Allah be upon him) said:

“Whilst I was lying near the Ka‘bah in a state between sleep and wakefulness, (an angel recognized me) as the man resting between two men. A golden basin filled with wisdom and faith was brought to me, and my body from the upper part of my chest to the lower part of my abdomen was split open and washed with Zamzam water, then (my heart) was filled with wisdom and faith. Then al-Buraq, a white animal smaller than a mule and bigger than a donkey, was brought to me. I set out with Jibril until we came to the lowest heaven. It was said: Who is this? He said: Jibril. It was said: Who is with you? He said: Muhammad. It was said: Has he been sent for? He said: Yes. He said: Welcome to him, what a blessed arrival. I came to Adam and greeted him with salaam, and he said: Welcome to you, as a son and Prophet…

Then we came to the seventh heaven. It was said: It was said: Who is this? He said: Jibril. It was said: Who is with you? He said: Muhammad. It was said: Has he been sent for? He said: Yes. He said: Welcome to him, what a blessed arrival. I came to Ibrahim and greeted him with salaam, and he said: Welcome to you, as a son and Prophet. Then I was taken up to the Oft-Frequented House (al-Bayt al-Ma‘mur). I asked Jibril (about it) and he said: This is the Oft-Frequented House; every day seventy thousand angels pray in it, and when they depart they never come back to it again.

Narrated by al-Bukhari (3207) and Muslim (164).

Al-Hafiz Ibn Hajar (may Allah have mercy on him) said:

Most of the reports say that it is in the seventh heaven. There is another report with a different isnad from Anas, attributed to the Prophet (blessings and peace of Allah be upon him), which says that it is in the fourth heaven. This was stated definitively by our shaykh in al-Qamus."(Fath al-Bari  66/309).

As for the existence of an animal meeting the description mentioned in the question, we have not come across any basis for that.

And Allah knows best.