I believe the answer is:
1. Ivan Ilyich wanted to weep, wanted to be petted and cried over, and then his colleague Shebek would come, and instead of weeping and being petted, Ivan Ilyich would assume a serious, severe, and profound air.
2. "This falsity around him and within him did more than anything else to poison his last days
From the first sentence, the narrator infer that even when a member of rising middle class is experiencing grief, they are forced to hide it due to the concern of their social standing.
From the second sentence, the narrator infers that unability to express emotion started to eating them from the inside and make them miserable.
Try replacing the word woman with any of those four words. Try to simplify the passage over all, and which ever one makes sense, is the right one. I'm assuming weakness is correct, because it says "therefore i forbid my tears" claiming they wont cry, and in this world, crying is a sign of weakness. But i would just get a few more opinions on it :)
There's a good answer to that question.
This is right because I don't really know if there're is a real word.