Another question I'd like answered is
What does Jekyll say about the dual nature of man?
In Dr. Lanyon's presence, Hyde drinks the potion in front of Lanyon because he is exercising his evil nature. The disturbing nature of the transformation greatly shocks Lanyon. This leads to his illness and eventual demise.
Jekyll had asked Lanyon to fetch hi potion/elixir. When Lanyon gets back Hyde is standing there. Hyde wants to shock Lanyon to witness a scene that would "stagger the unbelief of Satan." Lanyon, although disliking Hyde, is inquisitive and wants to see.
Your other question- This would take time but simply, he felt man has a good and bad side to his personality. He wanted to indulge fully in the bad side and realize all his hidden desires.
