clefs, sharps, flats, naturals
These developed from letters of the alphabet. The treble clef is a G clef, the bass clef is an F clef, and the tenor and alto clefs are C clefs. The signs denote which line has the respective pitch, and they derive from the corresponding letter. Historically, they could be used on any line of the staff.
Sharps, flats, and naturals all derive from the letter "B" because 1000 years ago, B was the only note that could have a chromatic alteration. The lower pitch was designated by a round b, also called "soft b" or "b mollum" in Latin, while the higher pitch was designated by a square b, also called "hard b" or "b durum." The round b sign was used at the beginning of the staff like a modern key signature or immediately preceding a notated B like a modern accidental to show that the lower B should be used instead of the higher one. In later centuries this sign was applied to other notes to indicate chromatic lowering, then it began to be applied to pitches other than B in key signatures. Later still, the sharp sign, derived from the square b, came to be used for chromatic raising, and subsequently in key signatures. Originally, sharps were used to cancel flats and vice versa, but as music became more chromatic this grew confusing, and the natural sign was developed, also derived from the square b.
(The square b was reinterpreted in German-speaking Europe as the letter h, accounting for the German names of B flat and B natural being B and H.)
notes, and pauses
These originated as dots and squiggles (called "neumes") to indicate melodic patterns. Stems were added, originally to identify longer notes, and rhythmic notation grew to include open and filled note heads, different color notes (subsequently abandoned), and hooks on note stems as additional mechanisms for indicating duration.
Meanwhile, people started using a horizontal line to help orient the reader with respect to rising and falling pitches in the patterns shown by the neumes. This expanded to four lines by about 1000 years ago, and then five lines or even more, eventually being standardized at five lines except for ecclesiastical chant, which continues to use four-line staves in neumatic notation. Each line or space corresponded to one note of the scale (as today), and to tell the reader where the half steps were, either C or F was marked at the beginning of the staff, which became the C and F clefs. The G clef appeared somewhat later.
and their locations on the stave
As you might guess from the previous sentence, the location of the clefs was arbitrary (though they were always placed on a line). It was only through tradition that the present locations were standardized.
Did they represent something, for instance something solid, like an object, of some sort, at some point?
Only inasmuch as alphabetic letters seem to derive from hieroglyphs -- for example, the name of B derives ultimately from a Semitic word seen today in Hebrew and Arabic as beth, beit, bayit, and bayt (compare Greek beta), meaning "house," and the form comes from a hieroglyph denoting a building. But this connection to an object was long since lost to abstraction by the time letters of the alphabet were applied to a musical scale.