1. A test fire primarily establishes proof that a firearm is in good and safe operational condition. It demonstrates that all processes of the cycle of operations are functional and in working order. Secondarily, a test fire may also include factors beyond the moving parts of a firearm, such as new or adjusted sights, the feel of different accessories such as grips and shrouds, and performance of different ammunition and external ballistic conditions. The overall performance and function of the firearm is benchmarked during a test fire.
2. There are numerous ways to increase safety when testing an unfamiliar firearm. Some research methods can aid, such as searching for videos if anyone has fired a particular gun before and posted their take on it. This can establish a "what to expect" benchmark. Owners often discuss problems they have encountered as well, giving more of a heads-up of what to expect. There are remote trigger devices which can be used to pull the trigger from behind a shield or enclosure, though at that point I would think the suspicion of catastrophic failure is high enough that it should not be fired to begin with. More tactile methods include wearing heavier protective PPE gear such as aprons, face shields, and gloves. These are beyond the typical "eyes and ears" protective gear associated with casual shooting. I believe the biggest asset when testing an unfamiliar firearm is to follow the book on safety and to stop if there is any doubt. Make sure the breech and barrel are undamaged, the ammunition is factory loaded, the firearm is in good operating condition, and that all safety protocols are followed. Skip no steps and take no shortcuts when it comes to inspection and safety. And maintain good equipment to not miss something important due to lack of tools or tool quality. I had to follow the test firing process on my .22LR Marlin SB when I had to replace a shattered receiver block and it is a bit unnerving to fire it that first time. But having dry ran it and tested it many times, I felt confident it was in good order, and it has been perfect ever since.

Respond like speaking to a friend in a short paragraph.