You can be infected with HIV only if an infected person hurt himself with the same nail not more than several minutes before you. Blood on the nail needs to be fresh because the HIV virus can stay alive for a very short time (several minutes) outside the human body when exposed to environmental factors.
We can never be sure how long HIV can stay alive on the razor and when exactly the razor was contaminated so it is better not to use a foreign razor.
If someone has sex very frequently it doesn't mean that he/she has HIV/AIDS. We can only say that persons who have unprotected sex have a higher risk to get infected with HIV. Protected sex (using condom) even with many partners is safer than unprotected sex with one person.
HIV-infection can't be diagnosed with simple blood tests like a complete blood count. You can request specific HIV-tests (ELISA or Western Blot) to check if you are infected or not. You should also repeat the test 6 months later.