Bismillah arRhaman arRahim
I read the article and I must say that I was not impressed. The author seems to base some of his theory on the work of a guy called Harun Yahya. I don't know if you know him but his real name is Adnan Oktar and he is a untrustworthy fellow. He warrants a thread of his own so I will rest his case. The author of the article uses no sahih hadith or Quran to back his claims, just some obscure opinions of some scholars.
Anyways back to the topic: as much as I have read on the topic of the end of times and the emergence of Imam Mahdi I can say the following:
1) This Ummah is going to be the last Ummah on earth. Thus the end of this Ummah will occur towards the end of times. The End of Times is one of those things which is classified as being part of Ilm ul Ghaib. This means that none but Allah (SWT) has complete knowledge regarding it.
They ask you, [O Muhammad], about the Hour: when is its arrival? Say, "Its knowledge is only with my Lord. None will reveal its time except Him. It lays heavily upon the heavens and the earth. It will not come upon you except unexpectedly." They ask you as if you are familiar with it. Say, "Its knowledge is only with Allah , but most of the people do not know."
[Surah Al Araf ayah 187]
Thus from this we gain that calculating when the End of Times is going to occur is a waste of time.
What we do know is that we are living closer to the End of Times as compared to the other Ummats that passed before us and that a relatively short period of time is left for the Last Hour. Exactly how short it is is known only to Allah (SWT).
2) Imam Mahdi has been described in the Ahadeeth as an individual from the family of Nabi Muhammad (SAW) who will appear suddenly towards the end. His name will be Muhammad. His coming will be preceded by great disunity amongst Muslims and the spread of injustice and violence throughout the world. He himself will not know that he is the Mahdi till the night before his appearance.
He will be performing tawaaf when he will be recognized. People will rush to pledge allegiance to him between Hajar al Aswad and Maqam Ibraheem. Armies will be sent out against him and will be destroyed. He will rule over the Muslims for a few years (7 I think) and will spread justice and peace throughout the world and will be present when Hazrat Isa returns. He will lead Hazrat Isa in salah.
There are many ahadeeth (some sahih...others not so much) regarding the Mahdi and describe him in detail. As to his coming only Allah (SWT) knows when.
3) I think think that when the Mahdi comes all true Muslims will know in their hearts that he is truly here. Besides that the descriptions of him in the Ahadeeth and the events that will follow him should be sufficient in guiding us.
Once he appears I think that every Muslim should try and pledge allegiance to him and follow his every instruction. Even if some Muslims are unable to reach him...I am pretty sure he will reach them
But since we do not know when he is going to come we should not give up in despair...seeing all the misery around us but rather try to spread justice and peace everywhere. There is work to be done and the responsibility is ours to do it. The Mahdi will simply be that shining light that will come when the world will seem darkest. That is something to look forward to...to know that when things will be at their worst we can expect a savior. As long as he does not come then perhaps things are not yet so bad
For more info check out Before and After the Last Hour by Ibn Kathir.
Wallahu a'lam