Can heuristic methods and machine learning approaches be considered alternate methods to solve NP-Complete problems?
I haven't seen these lectures, but here's what I think about he questions you pose.


No. NP-completeness is unrelated to the existence of algorithms. For example, we have plenty of problems that we can prove only have an exponential solution. We typically talk about "is there a solution" as decidability. There are problems that have no solution and we call these undecidable. The Halting Problem is a popular example.
Absolutely. When we can't find an efficient solution for all inputs, we find something that works for "most cases". In some cases, we can can prove the solution generated is not worse than K times the true optimal solution. In other cases, we cannot.
Yes.  Machine learning works well for certain classes of problems, but is really hard to apply to others.  It's not a "silver bullet" or alternate solution to computational complexity.


Regards.