No, a preexisting attorney-client relationship isn't always required. Offering advice pertaining to the application of laws or regulations to a specific person's facts is generally considered offering legal advice.
Some states regulate this very heavily, others don't care as much. Generally, California tends to regulate this pretty heavily for lawyers (for purposes of creating an attorney-client relationships that can subject them to malpractice claims) but otherwise not at all for non-lawyers unless they specifically hold themselves out to be in the business of providing legal advice (very common with immigration issues). So, offering random advice on the internet wouldn't be an issue for a non-lawyer (but could be one for a practicing lawyer if they get too specific).
My understanding (that is, I was told by a lawyer I know) is that if the person receiving the information thinks there's an attorney-client relationship, there is. Presumably there's some defense of "a reasonable person wouldn't have thought that", but this is why lawyers tend to be very diligent about saying "this is not legal advice".
Payment is generally not required to establish an attorney-client relationship.
> Are you a client? Was this directed at you?
No, but I'm looking at it from the perspective of the poster it was directed at.