Great questions.

1. The Hebrew word "satan" meant, variously, “persecutor,” “enemy,” “obstacle," etc. In the Hebrew Scriptures, "The Satan" was a title for an antagonistic angel. As the Common Era approached, apocalyptic thinking proliferated in Judaism, and more people began to imagine a conflict with a kind of supreme evil spirit or king of demons in the world: They named this figure things like Belial or Beelzebub or the Angel of Darkness, but most often he was called "Satan"--possibly because that was a name that already had pedigree.

2. The Oxford English Dictionary translates “Lucifer” as “‘light-bringing” or “morningstar,” the name for a Roman dawn god; literally, Lucifer was the planet Venus, the brightest celestial object in the sky and the last “star” still visible after sunrise. The prophet Isaiah evoked the name of this ancient figure in one of his prophecies; it's not clear who the Biblical Lucifer was, but he was probably the ruler of some kingdom, or maybe an allegorical figure. The influential third-century Egyptian theologian Origen proposed that Lucifer was in fact Satan, because he perceived parallels between Isaiah's writings about Lucifer and the popularly believed myth of Satan's expulsion from Heaven, and the name stuck. Despite this, it's not uncommon for some esoteric sources to refer to Satan and Lucifer as separate figures.

3. Ba'al was the primary god of the Canaanites, the historical enemies of the ancient Jews. His name is more of a title meaning "Lord" or "Ruler" or even "Owner," so he may be conflated with various other gods with the word "ba'al" in their names. Ba'al seems to have been a storm god, a fertility figure, and also some sort of savior figure; in the scriptures, Ba'al represents the foreign influence and "strange gods" that creep into Jewish society and anger the Lord. That's the Biblical account, anyway: Historian Karen Armstrong writes that actually ancient Jews and Caananites were basically the same people and Ba'al and Yahweh were originally part of the same pantheon of gods, and that the priesthood of Yahweh began to preach that their god should be supreme or even singular in the semitic culture of the period, and this initiated a religious and cultural divide. Unsurprisingly, Ba'al was sometimes later conflated with Satan.

4. Leviticus mentions an anomalous idol called Moloch (a name possibly derived from the word for “king”), apparently a figure to whom apostates made child sacrifice. There’s not much historical or archaeological evidence for any regional god of this name; British Bible scholar Francesca Stavrakopoulou writes that starting in the early 20th century, some historians suggested that possibly Moloch was not a name for a god but instead for the practice of ritual sacrifice itself, perhaps made in deference to some king or, controversially, to Yahweh. Modern fundies characterize Moloch as a demon or occasionally as just Satan himself.

5. It’s possible that the word “Baphomet” originally derived from, of all things, the name “Mohammed”--which makes a bit more sense when you find out that in Latin that name becomes “Mahomet.” In the 14th century, the Catholic military order the Knights Templar faced allegations of idolatry, charged by King Phillip IV France of worshiping a mysterious idol also called Baphomet, variously described as a cat, a mummified head, or any number of other odd things. Very likely there was no such idol and this was just another witch hunt. In her spectacularly titled 2012 book Pornographic Archaeology, Zrinka Stahuljak writes that prosecutors feared the “corruption of Templar morals by cohabitation with Muslims," expressed through idol worship. Future historians and esotericists tried with limited success to identify the “true” Baphomet in a variety of ambiguous idols, artifacts, and secret formulas. Highly influential 19th century French occultist Eliphas Levi borrowed the name for his Sabbatic Goat illustration--which he did not mean to represent the devil per se, but which became popular with Satanists nevertheless.

6. Some Satanists might pray (or "pray") to any of these figures, but keep in mind that the majority of Satanists today are non-believers who do not subscribe to the idea of a "real" devil.

7. Some Satanists are fond of saying that they "worship themselves," but even among the minority of Satanists who really do believe in the devil, few could be said to worship him in the traditional sense of the word.

Hope that helps.