Yes, Paul preaches Christ crucified, the Christian's dying and rising savior deity, not the historical Jesus, about whom he very oddly says next to nothing.

How do we know about what happened in Christianity right after Jesus's death, about the coming of the holy spirit, Peter's church and so on? From the later writings, such as Acts (which critical historians dismiss for being mostly propaganda). And when were those writings written?

Again, you're talking about "the gospel," as in the Christian good news in general, whereas I'm talking about the four canonical Gospel narratives. Do you understand the difference between those two things? According to scholarly consensus, four decades passed between Jesus's death and the first of those four gospels. The others were probably written on the basis of Mark. And none were eyewitness accounts.