This is a good video:
1) Indefinitely, but the virus is not really alive. It is a piece of self assembling genetic code. "Floating around in the blood" it is assembled. On cell entry the envelope is shed and it "Falls to bits", then there is replication/reassembly and exocytosis. There is a lot of waste. All the negative strands of RNA go to waste and are digested and recycled. A lot of the proteins suffer the same fate. The replicon unit has a lifespan of about 4 weeks (inhibited) but this is a half-life meaning it is an exponential decay over time with 1/2 at X units of time, 1/4 at 2 X units of time, 1/8 at 3 X units of time, etc
2) NS5B inhibition by Sofosbuvir is suicide inhibition - the sofosbuvir binds permanently rendering that replicon inactive. In time it will decay and be recycled. NS5A inhibition is transient, ie only while the drug is at a sufficient concentration, and it works by competing for space like a night club security person standing in a door blocking entry.
3) We use the Polymerase Chain Reaction to clone the HEP C RNA. We then look for specific target sequences in that RNA using probes that are like the mirror image of what we want to find.
4) Some membrane is used by the virus for it's capsule. Cell death occurs when the body's immune system recognises the infection and destroys the infected cell. This releases enzymes from inside liver cells like ALT/AST. Many cell lines (other than liver cells) are infected, thus the extra-hepatic manifestations
5) Harvoni is 2 things. Sofosbuvir suicide inhibiting NS5B and Ledipasvir competitively inhibiting NS5A. The drugs are well targeted at viral proteins but almost certainly bind to some host protiens and cause issues. These issues produce the side effects and depend on the genetics of the patient. The drug trials establish that we can successfully kill the virus without accidentally killing the patient. This is the trick with new drugs - get the effect desired without (too many) side effects.
6) Sofosbuvir is a pro-drug. It has no effect on anything and needs to be phosphorylated (twice) by CES1 and CatA to become the active metabolite GS-331007 which has a 1/2 life of 27 hours and exits via both the liver and renal (kidney) excretion - thus the problem with Sofosbuvir in renal failure patients.
I expect you may enjoy the detail in the European Medicines Agency Public Assessment Report: