Question 1: I read a claim that using Apivar for Varroa mite control also helps control Small Hive Beetle.
I have not found any support for this assertion here or elsewhere.
Can anyone confirm or deny?
Question 2: What is the current understanding of the impact of an Apivar treatment on Queen function (including sperm viability)?
Small hive beetles are insects. Since bees are also insects you don't want to use any mite treatment that works as an insecticide. Varroa are mites. They are not insects. Apivar is a miticide.
Not really. The active ingredient, amitraz is both an acaricide and insecticide. There are products w/ amitraz labelled for use against insects such as psyllids and lice. The difference is in the dose and delivery method. Apivar is designed w/ a dose-delivery mechanism that maintains an effective dose to kill mites. This dose is below the effective dose needed to kill SHB and bees and/or may not provide the proper exposure route). You could certainly use amitraz to kill SHB if the dose and delivery mechanism were correct. But, as you state, that would kill the bees too.
I would suspect that the originator of the Apivar and SHB statement was conflating Apivar use w/ that of amitraz use for other insects.