Peace be on you.
1=Ahmadiyya-Muslims believe that they fulfill prophesies of Holy Quran and Holy Prophet (pbuh) for latter days' spiritual reforms:
Holy Quran
[ch62:v3] He it is Who has raised among the Unlettered
people a Messenger from among themselves who recites unto them His verses, and purifies them, and teaches them the Book and wisdom, although they had been, before, in manifest misguidance;
[ch62:v4]And
among others from among them, who have not yet joined them. He is the Mighty, the Wise.
ABOUT THE VERSE (62:4) HOLY PROPHET (PBUH) EXPLAINED
The Companion Abu Hurairah (may Allah be pleased with him) said: One day we were sitting with Holy Prophet when Surah Jumua was revealed. I enquired from the Holy Prophet, Who are the people to whom the words, "And among others who have not yet joined them" Salman, the Persian was sitting among us. Upon my repeated asking him the same question the Holy Prophet put his hand on Salman and said;If faith were to go up to the Pleiades, a man from these would surely find it.
[Ref: Book of Hadith, Bukhari]
Along with other prophecies, the promised servant and ardent devotee has come with spiritual titles
The Promised Messiah and Mahdi to bring back the weakened faith with prayers, reforms, pen and services and no use of force.
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2= Moreover, Ahmadiyya-Muslims believe that following prophecies too are fulfilled in their Khilafat:
Holy Quran
[ch24:v56] Allah has promised to those among you who believe and do good works that He will surely make them Successors in the earth, as He made Successors (from among) those who were before them; and that he will surely establish for them their religion which He has chosen for them; and that He will surely give them in exchange security (and peace) after their fear: They will worship Me, (and) they will not associate anything with Me. Then whoso is ungrateful after that, they will be rebellious.
Holy Prophet (s.a.w.) foretold about two period of Khilafat after him [Its appearance, disappearance and re emergence]
a- “Prophethood will remain among you as long as Allah wills. Then Allah, the Exalted will take it away.”
b- “Then Khilafat on the lines of Prophethood shall commence as long as Allah wills. Then Allah, the Exalted will take away this.”
c-“Then tyrannical monarchy would be established, it will be there as long as Allah wills. Then Allah, the Exalted will take it away.”
d- “Then despotic kingship would emerge. It will stay as long as Allah wills. Then Allah, the Exalted will take it away.”
e-“Then (again), Khilafat on the precept of Prophethood shall be established. Then he became silent.”
[Ref: Narrated by Hadhrat Hudhayfa (r.a), Musnad Ahmad, Mishkaat]
Thus, by the grace of Allah the Exalted, Ahmadiyya-Muslims believe they are the Promised peaceful renaissance of true Islam in this latter days [1000 years] era.
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3= The following link will answer another part of the OP:
Post # 3 @ http://www.religiousforums.com/threads/ahmadis-and-baháulláh.183431/
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4= One does not see any similarity b/n the two movements except that both began in a certain part of the world and in time proximity.
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5= It is not a new religion.
Ahmadiyya Promised Messiah Mahdi (on whom be peace) wrote:
'This humble one has been sent for the sole purpose of conveying to God's creatures that, of all the faiths present in the world, the true faith which is in accord with the Divine will is the one which has been brought by the Holy Qur'an, and that the door that opens into the house of salvation is:
لا الہ الا اللہ محمد رسول اللہ
'There is none worthy of worship except Allah, Muhammad is the Messenger of Allah.'
(Essence of Islam, Vol. IV, p. 113 @ alislamDOTorg)
Under the peaceful non-political Khilafat, Ahmadiyya-Muslims aim to take the message of true Islam worldwide, and strive for international peace.
https://www.alislam.org/library/books/World-Crisis-and-Pathway-to-Peace.pdf
Against all possible resistances, they have reached in 209 countries of the world since 1889, by the grace of Allah the Exalted.
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