No, only retroviruses (like HIV, for example) do this which is why they have a reverse transcriptase enzyme that makes a DNA copy of their RNA genome. All other RNA viruses have an RNA-dependent RNA-polymerase (RdRp) which directly makes complementary RNAs from a single stranded RNA template. At some point in this process, a double stranded RNA intermediate is formed which is the specific form recognized by the RNAi machinery.

sometimes several different ones that work as pseudo “chromosomes”? and ¿sometimes a different DNA copy to make RNA genome copies?

You might be thinking, again, of retroviruses which integrate their genome, once in DNA form, into the genome of the host cell (e.g. HIV), or pararetroviruses who's genome, in DNA form, stays in the nucleus of the host cell, but not integrated into the genome (e.g. Hepatitis B virus). This is sometimes called a "minichromosome". From all of these, mRNA is made to translate into proteins, and new RNA genome copies are created which leave the cell as parts of the newly created viruses (or which are first copied back to DNA in the case of pararetroviruses).

The main thing I remember about virology is that is a clusterfuck of different systems.

It does integrate a lot of branches of biology and requires quite a bit of interdisciplinarity, and you have to deal with the host, virus and the environment at the same time - which is partly why I like it so much.

if RNAi is now a blanket term for all or several of those, or it’s a specific one.

RNAi is the name for the specific mechanism, it can perform multiple functions - like immunity and regulation, but there are of course other immune and regulatory mechanisms. Regulatory RNAi controls gene expression by recognizing hairpins and other double stranded structures in mRNA, to create the short targeting RNAs to either methylate the DNA genome (mostly just in plants), methylate histones, degrade mRNA or block translation on ribosomes - all of which lower the expression of the targeted gene.

Of course, there's a lot more complexity here, but I hope I'm explaining it at least somewhat decently.