What are the advantages and disadvantages of using rna or protein as genetic material?

The most important idea is that the genetic material of any organism must be able to accurately replicate itself at least every generation (or for multicellular organisms at each cell division).  

Base pairing (A-T or U and C-G)allows DNA and RNA (eg in polio virus, see Wikipedia page on RNA dependent RNA polymerase) to create a copy of themselves, when the appropriate enzymes are present. Proteins have no way of making a copy of themselves.  

Stability is probably the main reason DNA is the most common genetic material. DNA has no enzymatic activity and was probably selected for to maintain the integrity of the genetic material (rather than having to perform a function for the cell/virus, during which it may be destroyed). The double helix structure also protects its integrity, and proofreading enzymes have also evolved which correct most of the mistakes made at DNA replication. RNA viruses don't have this mechanism- which could be said to be an advantage (as they can rapidly change and therefore avoid their hosts' immune systems), however in non-parasitic organisms most mutations in a gene would lead to a loss of an essential function and the extinction of that genome.  

I don't think either of these reasons are relevant, but I think the main reasons retroviruses convert their RNA to DNA are so they can use the host cell's replication machinery (this was they do not need to encode as many genes), and secondly they need avoid the antiviral mechanisms of the cell, which would destroy any double stranded RNA molecules found (even if the virus was single stranded, dsRNA would have to be produced at replication).  

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not necessarily. higher fitness requires the organism to be reproductive successful. for example, an organism at age 10 with 15 offspring is much more fit than an organism at age 15 with only 5 offspring.