The EU still has both those barriers, that many of their countries guard their work permits more fiercely than their own balls, and their wages are lower than places like Dubai with far easier to get work visa. If the EU isn't careful their cake will be stolen by authoritarian places like Singapore and Dubai that have comparatively free trade and easy work permits.
Imagine that H-1Bs would be available in unlimited quantities any time of the year, as long as you meet the minimum requirements. And that the H-1B would be extended to a green card after a few years, assuming the authorities don't find anything too bad in the background checks. That's how it works in the EU.
European countries are generally more protectionist about working class jobs than professional jobs. If you have the education, skills, and experience, they assume that your presence would be good for the economy. And the citizens don't really complain. I guess a major reason is that the primary identities are national, while legal rights are EU-wide. If there are already hundreds of millions of foreigners who could apply for the same jobs, who cares about a small number of additional immigrants.
Yet somehow I've met barbers, janitors and vagrants who brag about tossing their passports on the way to the EU, while my Vietnamese neighbors (a practicing doctor couple in Vietnam), or American and Australian friends, found it extremely difficult to maintain their residency through legal routes, due to some non-issue. Some of them actually went to Dubai and Singapore, while the doctors ended up practicing in Switzerland instead.
I'm not saying that work-based immigration to the EU is easy. I'm only saying that the obstacles are not nearly as bad as in the US.
b.) Yes, it's insanely difficult, that's why the government should be making it EASIER for them to migrate, not flood with more paperwork. For instance, the UAE and Qatar have a Golden Visa programme that, upon verification of credentials by a govt-authorized background check company , grants a 10 year visa to doctors, high earners and uniquely skilled talents. Even nurses and pharmacists benefit from the programme and get the visa easily. The govt takes the effort to conduct the background check, instead of making them try to find employment first before coming to the country.
c.) My anecdotes were about clear and blatant, no regrets immigration FRAUD.