I haven’t done much MS, but many pharmaceutical companies have GCs with both diode-array and flame-ionization detectors; whether you turn one or the other on depends on the method you are doing, but both are often possible. These instruments are modular, so generally buying one part or the other and swapping them out is doable, it’s just a matter of what you need it for.
You can change the column too, and you can also change the mobile phase; the gas that you use to push your sample through the column, as well as vary it’s flow rate, column length and even temperature. All of these things can provide better peak resolution and definition, though might have down sides also (degradation of the sample, mobile phase peaks showing up with things that elute early, etc). The same is true for liquid chromatography, with a much broader range of mobile phases possible (mixtures, changes throughout the run, polar/nonpolar ratios, organic/nonorganic ratios, etc), as well as a large variety of columns.
Identifying a completely unknown molecule is time-and-resource consuming, but it isn’t particularly hard for people who know what they are doing (I didn’t stick to working as a chemist to be particularly good at this, but some of my coworkers were amazing). MS can give you molecular weight, which right off the bat gives you a large but finite number of possibilities. Molecules break up in the MS process in fairly predictable ways, so peaks of, say, 27 are likely C2H3, while peaks at weights of 46 are likely NO2. Given the ratio of common to uncommon isotopes (and that most peaks have little adjacent ones), then unless your mystery molecule is made up completely of rare isotopes, you can rely on tables of this sort to get some idea of what fragments you have. From there you can begin to piece together a puzzle.
FTIR can give you more information: the frequencies you obtain off of that can tell you how some of your fragments are more likely to be put together, because sometimes bits adjacent to other bits move one way while setting them up differently makes them move another way. I think MS is more useful overall for identifying unknowns, but FTIR can help and is faster and cheaper to do.
NMR can tell you pretty much anything you need to know about the molecular structure of something; it can be exceedingly complex to unravel the results, but running at different frequencies or using more precise instrumentation can give you a lot of information. I never developed the skills to be very competent with NMR, though my undergrad thesis advisor was amazing at it.
Then you can look at physical properties: what does it dissolve in? What is it’s melting point, what kind of reaction does it have with chemicals used to identify known classes of drugs/molecules? All this can help you narrow down what you have. If all your testing makes something look a lot like an opioid, then odds are you have an opioid with a few modifications to it, rather than some wholly unknown structure.
Spectroscopy is a pretty cool field.