http://reason.com/volokh/2019/01/15/man ... -foreign-s[1.] Federal law, 18 U.S.C. § 922(g), bans gun and ammunition possession not just by felons, illegal aliens, illegal drug users, and the like, but also by aliens who have been perfectly legally "admitted to the United States under a nonimmigrant visa."
[2.] "Possess[ing]" and "receiv[ing]" has been viewed as including temporary rental of a gun at a shooting range; indeed, that was one of the bases for prosecution in Rehaif. Rehaif was illegally present, but the statutory definition of possession and receipt would apply equally to all the categories of forbidden possessors and recipients, including people legally admitted under a nonimmigrant visa. Likewise, see U.S. v. Moussaoui (11th Cir. 2010), in which the defendant was indeed a legal visitor prosecuted for possession at a shooting range.
When I was a kid, we had exchange students stay with us on multiple occasions. Though I don't recall taking any of them to a shooting range, we could easily have done so.