Are there archaeological remains of the temple of Solomon?

Answer 1

Yes. Here is a news clipping that was published today (October 16, 2017).Quote:

Excavations conducted by the Israel Antiquities Authority (IAA), with the participation of volunteers, have uncovered large portions of courses of the Western Wall that have been hidden for 1,700 years.

The stone courses were presented at a press conference held Monday morning beneath the Tunnels' Wilson’s Arch. The press conference was conducted with the participation of Western Wall Rabbi Shmuel Rabinowitz, IAA Director Israel Hasson, Western Wall Heritage Foundation Director Mordechai (Suli) Eliav, IAA District Archaeologist Dr. Yuval Baruch, and the excavation's directors.

The stone courses, completely preserved, are built of massive stones and are outstanding in the quality of their construction.

Attached is the Related Link to the news source.

New Western Wall findings

Answer 2

Yes. They are visible adjacent to the Western Wall and the Mosque located in Jerusalem. The city is holy in four religions. Digging to uncover historical sites requires permission from the religions and the government, and has been carried out with care, for several decades.

Answer 3

Yes, remains from the Temple of Solomon, and the Second Temple, and the renovations added by Herod, are all visible at the Western Wall site in Jerusalem.