The wall you are speaking of is called the Kotel, more commonly known as the Western Wall. The men you see are not worshiping the wall because Jews are to only
worship G-d. The men (and women) are praying at the wall, quite often in sadness, because it is the last remnant of our Holy Temple (The Beit Hamikdash). It can be considered incredibly sad for us that there is no longer a Holy Temple and we remain living in exile.
The site of the Beit Hamikdash is still a holy site and yes, miracles have happened there from even before Temple times. The Beit Hamikdash is considered the center of the universe with regards the revelation of G-dliness in our world. It is the "dwelling place" of G-d. While the Holy Temple was standing, there were ten miracles that happened on a daily bases.
More information on the Temple Mount and miracles:
"Mount Moriah, according to Jewish tradition, is the place where many pivotal events in Jewish history took place. Traditionally, creation of the world began from the Foundation Stone at the peak of mountain. This is also where Adam, the first human, was created.
When Abraham was commanded to prepare his son Isaac for sacrifice, the father and son went up to “the place that G-d chooses” – Mount Moriah, and to its peak – the Foundation Stone – where the binding of Isaac took place.
Also Jacob’s dream with angels going up and down a ladder is linked to this mountain.
Later on, the Holy of Holies – the core and heart of the First and Second Temple - was built around the Foundation Stone."
From: the Kotel.org
More on the akediah
(binding of Issac)
May the Beit Hamikdash be speedily rebuilt in our days.