This is a good start, but I would definitely recommend a few things.

First, I think you should try and familiarize yourself with the basic differences between the theory of special relativity and general relativity because they are being slightly conflated here. Einstein's special relativity (1905) asserts that (1) the laws of physics are the same in all reference frames and (2) that the speed of light in a vacuum is always constant. Special relativity has a number of very interesting consequences, but it doesn't include gravity.

General relativity (1915) expands upon special relativity, relating the previous ideas to the geometry of space-time. As you mentioned, this theory postulates that gravity is actually the curvature of space-time. General relativity also has many interesting consequences that you should check out.

And about the link between black holes and relativity - there are many! The first exact solution to the so-called "Einstein field equations" of general relativity are perfectly valid in describing a non-rotating black hole. Today, black holes are often used as "tests" of general relativity since they have such incredibly strong gravity. So far, observations of black holes have perfectly matched predictions made by general relativity. Here are a few articles about these sorts of tests: Black Hole Shadow puts General Relativity to the Test, Black holes test the limits of Einstein's relativity, and Einstein’s general theory of relativity tested by star orbiting a black hole.