One would expect screening procedures to be in place. I don't know much about HCG or HIV. I read a Harvard Medical School newsletter on HCG and it mentioned a number of potential adverse reactions. The long-term outcome was suppose to be poor too due to a failure to change lifestyle, i.e., people making the same poor lifestyle choices.
You could always err on the side of caution and decide not to take it.
I think Dr Beckerman wrote a blog on HCG. You may like to check that one, and others, out.
No, because unless there is unusual circumstances (i.e blood in the urine) then the virus isn't passed along through urine, and even if there WAS a tiny risk in the undiluted product, the drops are so diluted that they don't even contain hcg anymore; just the essence/memory of it.