OK, about stereo 45's. Most sources I've consulted agree the first stereo 45 was "There Goes My Heart," by Joni James on MGM, around 1959. MGM made other stereo 45's as well; so did Liberty, ABC-Paramount, and others. They were a huge flop because the teens who bought 45's didn't have stereo players, while mom 'n' dad, who owned those big console stereos, didn't buy 45's. The stereo 45 was pretty much dead by about 1962, and stayed that way for almost a decade.
It was probably the need for stereo promo copies for FM use that brought back the stereo 45. Some labels still manufactured their store-stock 45's in mono only into the early-mid 70's (Bell, Parrot, maybe others.) And of course promos were usually stereo on one side,mono on the other.
As for stereo LPS, reissues of material recorded in mono to begin with (old jazz or classical, radio shows, etc.) were and still are released in mono; the "fake stereo" so popular in the 60's and 70's less prevalent now. As far as I know, Capitol never used Columbia's pressing plants; though Warner Bros. switched all their pressing from Columbia to Capitol in the mid-70's because Columbia was apparently slowing down on filling WB's orders in order to do them harm competitively. (You might remember WB singles suddenly having that Capitol raised-grooved rim around the label.)