1. I'm not sure that I agree. Not all research is a race against time. But, perhaps you're right, I'll accept this.
2. Certainly the most plausible thing we have now, I'm not sure that that makes it plausible, but better than anything else. so okay.
3. This depends on what you mean. Neural Networks are actually significantly easier to analyze than arbitrary programs, when you essentially restrict yourself to two operations (multiplication and sigmoid or ReLU), things get a lot easier to analyze. Here are some questions we can answer about a neural network that we can't about an arbitrary program: "Will this halt for this input?", "Will this halt for all inputs?", "What will a mild perturbation of this input have on the output?", these are as a consequence of fineiteness and differentiability, which are not attributes that a normal program has. (caveat: this gets more difficult with things like RNNs and NTMs, but afaik is still true). The questions that we find difficult answer for a Neural Network are very different than for a normal program: namely "How did this network arrive at these weights as opposed to these other ones?" and related "What does this weight or set of weights represent?", but I don't think that there's any indication that those questions are impossible to answer (and often we can answer them, like for facial recognition networks where we can clearly see that successive layers detect gradients, curves, facial features, and then eventually entire faces)
4. Agreed. There's no real reason to know why it works if it works.
5. I think you can tell, but I don't think this holds.