> With close microscopic examination of inclusions and defects, yes you probably can.

With good laboratory instrumentation, you might be able to distinguish between them -- i.e. note that they're not perfectly identical, that they are distinguishable -- but, unless you are an expert, you would be unable to tell which of the two is the natural stone.

So, practically speaking, it doesn't matter.

Yes, you need to know which features are evidence of mined vs. synthetic/lab grown. Although there is equipment now preloaded with software that can discriminate. I think its based on photoluminescence.