1. No, needing a license does not make it professional, but general, unfettered access certainly precludes professional status. Nowadays, when anyone can get any product online, the definition of a professional product seems elusive. And many companies that make professional products now also have consumer divisions (like CND, OPI, Orly), so it is more useful to think of a professional product rather than a professional company, although those certainly do exist. But I think you can still easily identify a professional product. A professional product is one that is designed with professional usage in mind and marketed to professionals through trade journals, professional shows and organizations, and that provides the appropriate professional supports - education, training, r&d, customer service, MSDS, associated products, etc.. Such products tend to be a bit harder to find and may still require certification, of a higher quality (remembering that quality often goes beyond what is in the bottle), and is often higher in price.
2. It is well known (and documented) that there is a problem with the regulatory environment in China that has allowed counterfeit, tainted, and even dangerous products onto the market. While many of the chemicals we use can be dangerous, the problem with many of the non-pro "brands" from China goes beyond the nail tech taking proper precautions and comes down to a fundamentally defective product.
3. There is no such thing as a universal lamp - it is really that simple. Utilizing a lamp universally does not make it universal, it just makes it dangerous. While they should learn that in tech school, it is also critical that they hear it in professional venues like this forum. Anyone who will not spend an additional $100-150 buying the proper lamp should be called out in this forum. When you recommended using the CND lamp as a universal lamp, you gave incorrect and misleading information and failed to take responsibility for educating our colleagues.