The EU doesn't make (much) real law per se. Unlike the USA, the EU doesn't really have a criminal system, or federal laws etc. The EU makes member states (which are countries and states) implement a law. This law would only apply to owners of websites. They don't block websites.
No, at worst an EU state might block your website.
But that won't happen either: it's a law that applies to EU companies with a website. Your company might have to worry a little if they chose to incorporate in Europe.
No, that's not true. Where a company is domiciled has nothing to do with these regulations - they apply to any company which has users in the EU. And yes, they will apply in a slightly different form as interpreted to each member state.
And yes, this is a somewhat ridiculous situation; but in practice it's not really likely to be a problem, unless you've got a major presence in an EU market.
In practice, the UK at least is extremely unlikely to pursue any non-UK companies for breaching the UK interpretation of these regulations (which is very light-touch anyway); if only because of the difficulty in taking effective action.
Other member states might take a more or less proactive approach in pursuing action; and other countries have a different take on the regulations anyway.
Basically, if I was a small-ish non-EU based website with EU customers I'd be keeping an eye on this to see where it goes, but I wouldn't take any action yet.
If I was a large non-EU-based site with tens of thousands or millions of EU customers, I'd be paying quite a lot of attention; what I did about it would depend on my risk profile.
