Rescue Disk and Equation Group malware

[Faust.]

About a decade ago Kaspersky revealed numerous pieces of malware that are unofficially attributed to the NSA.  "Fanny" was one of those. It exfiltrated information from air-gapped (not connected to the Internet) computers.

Three questions:

1. If my computer were infected with Fanny or its brethren and I were to connect to the Internet with Kaspersky Rescue Disk, would Fanny be able to exfiltrate information or "phone home"?

2. Can Kaspersky Rescue Disk detect hard disk controller firmware viruses?

3. Can Kaspersky Rescue Disk detect BIOS viruses?