Is saying "it seems he did some improper things" or "he did some improper things," and the subsequent words concerning my brother's relationship with a girl, considered a slander (qadhf) that necessitates the prescribed punishment (hadd), knowing that what was within me was doubt and conjecture, not certainty?

It is not permissible to accuse a brother or anyone else of committing indecency or forbidden acts without clear proof. The mentioned phrase does not constitute qadhf (slanderous accusation) that necessitates the prescribed punishment (حد). Qadhf is explicitly or implicitly accusing someone of zina (fornication/adultery) or making an insinuation that, with contextual evidence, indicates an intention to accuse of zina. One must repent to Allah for accusing the brother and the woman, and clarify that what was said was not true.