Both the shutdown and suspend issues were due to a recent kernel update. I reinstalled Ubuntu and both the issues were fixed.
But the wake-up issue was still there so I replaced Ubuntu with elementary OS. It didn't help: the wake-up issue was there as well. To fix wake-up issue, I installed the latest version of the kernel (5.4.6) on elementary OS and both the shutdown and suspend issues appeared again. So I had to downgrade the kernel version to remove them.
Now, I have installed kernel 4.19.79 (as instructed here) and the amdgpu-pro drivers provided by AMD. The wake-up issue has occurred once after the last nine suspends which is much better a situation than what it used to be (roughly once after every two suspends).