As you know, there are attacks on the firmware of BIOS and HDD. What if I used some kind of VMS, maybe VirtualBox? Will this protect me from an already infected BIOS (and by that, I mean, no one can steal my RSA private keys)? What if I can use the VM from Tails OS that does not touch the HDD? Will that protect me from infected BIOS and HDD so no one will be able to steal my keys using the infected HDD or BIOS?
Virtualization does not protect you when the host system is compromised.
An attacker who controls the host system, controls the execution of the hypervisor which means they control everything which happens in the virtual machine.
In theory... In practice, virtualization is an uncommon scenario for typical malware targets, so you will encounter few malware which contains a payload to attack virtual machines running on the host (although this isn't unheard of).
It all depends on how the virus acts and spreads itself. Apart from the well known attack vectors such as network connections and file sharing, viruses are able moves between guest and host OS for example by using the emulated virtual COM port.