Welcome to the forum and thanks for your question.
First, you describe a low risk event; testing for HIV or viral hepatitis is not recommended simply because someone gets a tattoo. Although acquiring blood borne infections was once a problem at some tattoo parlors, for the past 20-30 years these establishments have been more tightly regulated in all states and to my knowledge there have been few if any such infections reported in the US for many years.
To your specific questions:
1) If you have HCV, it had no effect on the reliabilty of your HIV test. The thread immediately before yours, asked the same question. Take a look: http://www.medhelp.org/posts/HIV-Prevention/Delayed-Seroconversion/show/1709580
2-4) Unfortunately, I can't help in interpreting your HCV test results. Contrary to popular beliefs, HCV is not considered an STD. Therefore, we don't regularly test for it in my STD clinic and I have little experience with the current testing methods and interpretation of the tests. From what I know, however, your tests do not indicate you caught HCV during the tattoo; if the second test is accurate, it probably resulted from some other, more recent exposure. I would recommend you follow your doctor's advice about it; or if you want a second opinion, ask for referral to an infectious diseases or gastroenterology/liver diease sepecialist.
Here is another thread that discusses sexual transmission of HCV, in case you are interested: http://www.medhelp.org/posts/HIV-Prevention/hcv-and-hiv/show/1324890
Best wishes-- HHH, MD