hartshorn
"Spirit of hartshorn, also simply hartshorn: the aqueous solution of ammomnia (whether obtained from harts' horns or otherwise). salt of hartshorn: carbonate of ammonia; smelling salts" (OED). A hart is another term for stag or deer. 
Smelling salts are "a preparation of carbonate of ammonia and scent for smelling, used as a restorative in cases of faintness or headache" (OED).
rubber
According to the OED, rubber refers to "A set of games (usually three or five), the last of which is played to decide between the opponents when each has won an equal number; (hence) the winning of more than half the individual games by one side" (OED).
This phrase altogether indicates that Lady Middleton was partaking in a card game upon hearing the news of Marianne.
indisposition
"Want of adaptation to some purpose, or to the circumstances of the case; unfitness, unsuitableness; incapacity, inability." (OED).
bely
"To deceive by lying, or to tell a lie" (OED).
Because you are so sly about it yourself, you think nobody else has any senses; but it is no such thing, I can tell you, for it has been known all over town this ever so long. I tell everybody of it and so does Charlotte.”
Example of how gossip plays a big role in society. Gossip is how information goes around and status can go up and down.
When they had paid their tribute of politeness by curtesying to the lady of the house
This was also custom and simple manners when attending a party. It is offensive if this action was dismissed. It is a way of introducing oneself to the host/hostess and showing gratitude for the invitation.
ascended the stairs, heard their names announced from one landing-place to another in an audible voice, and entered a room splendidly lit up
During this time, the purpose of this was just so that your presence was known and acknowledged. This is custom.