The UK's ICO also has a good structured summary: https://ico.org.uk/for-organisations/guide-to-the-general-da...
In general I agree with the sentiments in this article. I've probably spent a total of three to four days reading around the GDPR and I don't really see what's special about this law other than it's imposing decent standards on what was in effect a wildly unregulated industry in people's personal data. If you have a broad distrust of any government activity then I suppose any new laws with "fines up to €X" might feel like "I run a small site on a Digital Ocean droplet and I'm at risk of a €2m fine out of the blue." But that doesn't make it true.
There's nothing that says IRS won't prosecute you if someone buys you a soda and you don't declare it as income.
Or that you won't be prosecuted by someone in the US if your blog has a copyrighted image and you don't receive a DMCA request that was sent to you.
See how ridiculous that sounds?
All fines can be administratively and judicially appealed.