Origins
Much that is in Star Trek originated in much older Sci-Fi specifically the works of
E.E. "Doc" Smith. Some examples are below.
From the Skylark series. Ships are screened (the same as shields just a different name), tractor beams and pressor beams though I don't believe he used those names until he wrote
Triplanetary. Late in the Skylark series Smith introduced "translation" through the 4th dimension a.k.a. the transporter. It is also the earliest I recall seeing "green men" mentioned in Sci-Fi though they were not little.
The Lensman series (starting with Triplanetary as mentioned above) gave the tractor and pressor beams their names. It also introduced the "detector nullifier" which was a cloaking device in function though not name. Triplanetary itself included ships that were non detectable due to their shields. The series also introduced a ship called a "Mauler". Not the SFB mauler though I believe it to be the inspiration.
The Lensmen series had a ships weapon referred to as a Primary, a normal weapon overloaded. The source for overloading heavy weapons and the X-Phasor in SFB perhaps?
Triplanetary introduced a battle formation called the "Cone of Battle" (description quoted below).
Now, systematically and precisely, the great Cone of Battle was coming into being; a formation developed during the Jovian Wars while the forces of the Three Planets were fighting in space for their very civilizations' existence, and one never used since the last space-fleets of Jupiter's murderous hordes had been wiped out.
The mouth of that enormous hollow cone was a ring of scout patrols, the smallest and most agile vessels of the fleet. Behind them came a somewhat smaller ring of light cruisers, then rings of heavy cruisers and of light battleships, and finally of heavy battleships. At the apex of the cone, protected by all the other vessels of the formation and in best position to direct the battle, was the flagship. In this formation every vessel was free to use her every weapon, with a minimum of danger to her sister ships; and yet, when the gigantic main projectors were operated along the axis of the formation, from the entire vast circle of the cone's mouth there flamed a cylindrical field of force of such intolerable intensity that in it no conceivable substance could endure for a moment!
To me this appears to be the inspiration of the ISC eschelon formation.
The Lensman also introduced the Arisians, formerly humanoid entities of enormous mental powers which appear to be the source of the Organians. (The Lensman may also be the precursors of the Jedi.)
John W. Campbell Jr introduced the idea of FTL by means of warping space (also by warping time) in his Arcot, Morey and Wade series in
Invaders from the Infinite and
Islands of space.
Other Sci-Fi may perhaps predate some of this but these are the oldest that I recall. Does anyone recall any older sources?