يوم الدين = the day of the Faith = the time of Dissolution predicted by Islam as well as by Science. Sir Syed Ahmad fully explains the meaning of يوم الدين = Universal Destruction and of قيامت صغرى = individual destruction, (i.e., death) from the viewpoint of modern Science.
As regards miracles, the beliefs that are held do not matter so much as the spirit in which they are held. If the spirit is right and leads to virtuous conduct in life, any reasonable belief will quite do. Here comes in the Pragmatism of Islam. It does not object to anything which has a practical value unless it is unreasonable, immoral, or inconsistent with the Islamic ideas of the unity of God and the brotherhood of man.
"We will soon show them our sign in all horizons (= regions) and in their own souls, until it shall become quite clear to them that it is the Truth—Qur'an xli 53. سنريهم آيا تنا فى الا فاق و فى انفسهم حتىا يتبين لهم انه الحق
God's is the East and the West, therefore whichever side you turn, you will see the face (= presence) of God—Qur'an i. 115.
ولله المشر و المغرب فا ينما تولو فثم و جه الله
And He is within you (= in your mind), why don't you see Him?—Qur'an li. 21. و فى انفسهم افلا تبصرون