To answer the first part of your question:
Einstein's theory included predictions about the nature of black holes and the delays they would cause to light travelling through space, so astronomers will aim to compare the theory with the actual measured reality - the ultimate test of General Relativity. If the two are consistent, Einstein wins again. If not, then we know there is something missing in our understanding, opening up a whole new area of astrophysics.
In this case, SKA 101 will track a gravitational wave as it passes through the universe. How you may ask?
Their rapid and regular rotations (referring to pulsars) make pulsars incredibly precise space clocks, as accurate as the best atomic clocks on Earth. They emit a pulse of radio waves like a lighthouse beam, which radio telescopes can detect from Earth. It is this accuracy, and the SKA's ability to detect even the most subtle variations in this caused by a passing gravitational wave, which will hopefully enable this breakthrough in science.
The SKA will be able to time millisecond pulsars (which are both faster and rarer than an average pulsar) typically to 100-nanosecond precision, and even better in some cases. This means it can predict a pulse’s arrival time to better than 10,000,000th of a second, a level of accuracy which is essential to spot the tiny deviations caused by a gravitational wave.
By timing a whole array of pulsars, the SKA will effectively create a cosmic observatory, tracking a gravitational wave as it passes through our galaxy.
[Bracketed phrase is own annotation]
I will also answer @uhoh's question in the comments:
@ScienceAJ how exactly does SKA monitoring pulsars test general relativity in a way that all the other pulsar monitoring telescopes (radio or X-ray) can't? Just what kind of gravitational waves can SKA look for that the ever-widening array of gravitational wave detectors already looking can't?
Because SKA 101 is the best telescope for the job. It was built to test the theory too. For example, read this short paragraph:
Back in the early 1990s astronomers asked themselves what sort of telescope would be needed to investigate the astronomical questions of the new millennium. The answer: a radio telescope with a total collecting area of one square kilometre and 50 times the sensitivity of any existing telescope. From this came the concept of the Square Kilometre Array (SKA), a project that has drawn together scientists and governments from 20 different countries, and when completed in 2030, will be the world’s biggest radio telescope.
To answer your 2nd question:
The SKA telescopes will initially comprise 131,072 antennas in Australia (known as SKA-Low), which will be built at Inyarrimanha Ilgari Bundara, on Wajarri Country in Western Australia, and 197 dishes to be built in the Karoo in South Africa (known as the SKA-Mid).
When finished, the observatory will consist of thousands of dishes and up to a million low-frequency antennas that will enable astronomers to monitor the sky in unprecedented detail and explore the first billion years after the so-called ‘dark ages’ of the Universe.
I have yet to find out why having so many telescopes enables powerful precision though.