The Particle M-SoM documentation (M-SoM datasheet | Reference | Particle) lists two small antennas that are "approved" for use with the device. Is there an "approved" external antenna I can use somewhere? The breakout board clearly has SMA connectors that are ready for an external antenna.
What if we want to use a different antenna such as this directional one (Amazon.com)? What are the rules regarding this? I obviously don't want to get in to trouble with the FCC. If I'm not increasing the power of the transmitter, etc, can I just swap out the antennas? Are the rules different for personal/commercial use? If I do need some sort of certification, how do I go about that?
An antenna change to an antenna of a different type (not a trace antenna), or an antenna of a higher gain in any frequency band, generally requires recertification.
For hobbyists using a single device you will probably be OK using a reasonable alternate antenna. For example, the 4" long LTE whip antennas with a magnetic base and a SMA connector, intended for use in cars, work well.
The issue if you are making a product based on an alternate antenna. This will require FCC certification. All products require unintentional radiator testing of your completed assembly, but this is relatively easy and inexpensive. Changing the antenna requires intentional radiator certification, which is much more complicated and expensive.