...yep, I mean the gravity model of trade is just a regression. It is very unlike pretty much everything else in macro because its validity is statistical rather than theoretical (and more models that are justified by theory often perform worse...although this is kind of complex).
The Philips curve changes over time. It is, however, quite easily testable so it either applies or doesn't. If you are looking for some hard rule that applies every time then you should take an interest in something else (indeed, this was my initial point...the issue is that economists believe that the economy are a set of equations to be solved...in reality, the nature of the economy is changing constantly).
I don't think that is the case. Economists are confronted with the difficulty of tests everywhere (the issue is that they often don't handle this well), it is why econometrics is distinct from statistics. As an example, interest rates and growth are positively correlated (i.e. higher rates appear to cause higher growth)...we know this isn't the "true" relationship (interest rates are a function of expected growth) but there has been a ton of work done to separate these effects (this isn't only in macro, controlling for confounders/ommitted variables is really what econometrics is about). Econometrics is really the best part of economics.