The Keys of Solomon are two grimoires written in the 15th century and 17th century by anonymous authors but attributed pseudepigraphically to Solomon. There are numerous other Medieval/Renaissance grimoires attributed to Solomon, again pseudepigraphically and written by anonymous authors. Even before them was the Testament of Solomon written in Greek in about the 3rd century CE, again by anonymous authors pseudepigraphically.
The Temple of Solomon is a mythical temple that never existed, and it's an allegory for the soul.
Yes, Solomon never existed. All those books and the Temple you mentioned are either pseudepigraphical or mythical/fictitious.