Viral mRNA is translated on host cell ribosomes? Replication of viral RNA occurs in the host nucleus?

First answer to your question is yes! And the second answer to your question is yes AND no, it depends on the virus. For example HIV (once integrated in the host cell genome) can make viral mRNA in the cell nucleus and then later translated outside the nucleus of the cell (cytoplasm) in ribosomes. Many other viruses (besides HIV) just use the cytoplasm's machinary to synthesize all needed building blocks for viruses.