It is two separate conditions. Those conditions are:
- If it is practical to do so and
- Upon a reasonable and timely request
The two things on either side of the and are independent of one another.
Thus, the manage in charge can conduct a test firing of a firearm if they make a request that is both reasonable and timely (a word that can have multiple interpretations, and it's hard to be sure which is meant here), and it is practical to do so. The practicality test is of the test firing, not of the request; the tests applied to the request are just that it is reasonable and timely.