Great questions!

The short answers are: yes, there were Black owned and operated radio and television stations, though not in the early years of either and relatively few in number overall. In both cases, there was much more content produced by Black creators for Black audiences -- sometimes aired through mainstream networks, sometimes through separate/independent channels aimed at Black markets.

On radio, I recommend William Barlow's Voice Over: The Making of Black Radio. Black culture (and blackface minstrelsy...) was a major current in American popular culture writ large at the dawn of commercial radio -- after all, we colloquially refer to the period as "The Jazz Age." So it was common to hear Black cultural forms (music, comedy, etc.) on any radio station. 'Mainstream' radio stations, however, generally programmed with an exclusively white audience in mind, and would regularly use white performers to cover these works. Some did carry explicitly 'Negro' programming, though, by the late 1920s -- Jack Cooper's "The All Negro Hour" is noteworthy here. Cooper was particularly ambitious -- while I don't think he ever owned a broadcast station, he did control the entire production of his show (including, if I recall, ownership of the recording facilities).

(I don't think this is exactly what you meant by ownership/production, but as a bit of an aside: one significant turning point for Black artists in early-ish in radio history came about as a result of the ASCAP boycott: their new rival, BMI, was more willing to break the color line. This brought significantly more Black artists on commercial radio and, importantly, meant they could earn royalties -- an ownership stake in the content.)

I'll say a little about Black television in a second, but the more significant impact of television on Black media of the mid-century was from its indirect effects on commercial radio. Radio broadcasters saw an impending collapse of their business model with the popular adoption of television, and found themselves scrambling to evolve. This led to two critical developments: first, radio stations in urban markets began to experiment with a 'black appeal' format in the early 50s. Radio was largely decentralized and locally owned in the early- to mid-twentieth century, so a few of these stations were Black owned -- WERD in Atlanta was the first, in 1949 -- but most were not. Regardless of ownership, though, these were much more likely to be staffed and/or managed by Black operators, and offered programming aimed at black audiences. The second development was the adoption of almost exclusively musical formats. This was mostly done at first as a cost-saving measure (records were a lot cheaper than recording a radio drama), but it turned out to be the perfect format for car radios. And as it happened, cars were a domain where white suburban teenagers could experiment free of their parents' prying eyes. Between those two forces, these 'black appeal' stations and their programming (along with much more frequently Black-owned record stores) were absolutely foundational to the early development of rock and roll -- they created the audience and the market. For more on this, I recommend Altschuler's All Shook Up.

The barriers to entry for commercial television broadcasting meant that there was, to my knowledge, no Black owners of any stations or major production facilities during the first few decades of television. By the mid-1960s, however, media representation and ownership became major topics of concern for Black community leaders and activists of all stripes -- famously the Black Panthers published their own newspaper for this reason. There were also a number of efforts from Black creators at producing content for public/community access radio and television formats throughout this period: one well-documented example is Black Journal which began airing in 1968. (Devorah Heitner's Black Power TV provides a deep dive on Black Journal and a local show called Inside Bedford-Stuyvesant.) As for broadcast facilities, the first Black-owned television station was WGPR-TV in Detroit, which came on air in 1975. This was significant, and the station largely used Black talent both behind and in front of the camera. But it was also short-lived: cable television was already on the rise, and BET would debut five years later. WGPR-TV continued through the 1980s and had a bit of a cult following (side note: one of their most popular programs was Arab Voice of Detroit, if you're interested in other media by and for PoC), but their audience was always limited and they never expanded beyond the Detroit metro.

WGPR-TV got picked up by one of the Big 3 networks in the 1990s. Not to end on a down note, but that also serves as a bit of a coda to this whole thing: deregulation and consolidation in the late 20th century swept up many of the independent Black studios and almost all (of the already few) Black-owned broadcast stations. Of course, Black representation also increased substantially in 'mainstream' broadcast media over the same period -- though often in a 'universalized' or less racially specific format (white washed, if you prefer) -- so make of that tradeoff what you will.

Edit: Whoops! I said NOT to end on a down note. Obviously, some late twentieth century Black-owned broadcast endeavors were tremendously successful.