]1. Lydia mentions how horrid the Gardiners were to her when she stayed with them before her wedding, and adds, "...not a party or scheme or anything..." What is a scheme? Does it just mean a plan to go out, or something more specific to the time period?

I believe you are correct in your interpretation of it referring to plans to go out. Of course we know that the Gardiners were by no means horrid and mean to Lydia. Under the circumstances they were very prudent to keep her under wraps. Lydia who was always wanting to be going and doing and wanting to be seen perceives it this way seeing herself as a prisoner in their home. She has no sense of wrong-doing or the effects of her actions on her family. At some point, in a letter I believe, she was talking of attending balls even after she was married and dancing with all the officers, etc. which had me rolling my eyes upward. She hasn't even the tiniest ounce of decorum.

2. I believe I have heard it said that the person of higher rank must request the introduction: "Elizabeth had mentioned her (Lady C's) name to her mother, on her ladyship's entrance, though no request of introduction had been made." This would seem to confirm this rule of etiquette.

3. I don't know if it's appropriate for Mr. Bennet to be going off to his library or not but it seems rude to me. ;-0