I think we can get an idea of the tone of Jane & Emma’s tête-à-tête in Ch. 20 and the questions therein partly from the conversation between Emma and Mr. Knightley in Ch. 21. Emma was pleased with her “own perseverance in asking questions, and amused to think how little information” (21) she obtained from them which conjures a picture of her relentlessly peppering Jane with questions. Peppering a guest with questions for amusement does not seem the right thing for a hostess to do. If Emma knew Jane did not wish to confide her personal opinions, which her amusement suggests, then my feeling is she ought to have accepted it gracefully. I think as a guest Jane had an obligation to be polite and conversable—which she was although assuredly not to a degree acceptable to Emma.

Emma’s agenda and her manner, “quick and assured” (5) and mostly unrestrained (1) can suggest what kind of questions she asked Jane. She needed “real insight into Mr. Dixon's character” and Jane’s “value for his company” and a picture of the newlyweds’ relationship, “the suitableness of the match”, to verify her suspicions about them. I think questions about his sporting habits and enjoyment of parties and music is unlikely to give the kind of real insight Emma desires. I can’t suggest specific questions but I agree with Kathleen Glancy that they were probably direct and to the purpose as she was in obtaining information about Mr. Martin from Harriet (4). As with Harriet, Emma is motivated to discover and I don’t see why her manner of questioning would be different. What is seen of Emma’s manner in speaking to Jane seems usual—quick, assured and unrestrained:

"No -- I have never seen Mr. Elton," she replied, starting on this appeal; "is he -- is he a tall man?"

"Who shall answer that question?" cried Emma. "My father would say 'yes,' Mr. Knightley, 'no;' and Miss Bates and I that he is just the happy medium. When you have been here a little longer, Miss Fairfax, you will understand that Mr. Elton is the standard of perfection in Highbury, both in person and mind." (21)

"You are silent, Miss Fairfax -- but I hope you mean to take an interest in this news. You, who have been hearing and seeing so much of late on these subjects, who must have been so deep in the business on Miss Campbell's account -- we shall not excuse your being indifferent about Mr. Elton and Miss Hawkins." (21)

Also it seems Mr. Knightley was a witness to their conversation:

"No," said Mr. Knightley, nearly at the same time; "you are not often deficient; not often deficient either in manner or comprehension. I think you understand me, therefore."

An arch look expressed -- "I understand you well enough;" but she said only, "Miss Fairfax is reserved."

"I always told you she was -- a little; but you will soon overcome all that part of her reserve which ought to be overcome, all that has its foundation in diffidence. what arises from discretion must be honoured." (21)

Mr. Knightley noticed Jane’s reserve with Emma and suggests two reasons for it—diffidence: “distrust; want of confidence” and discretion: “Prudence; knowledge to govern or direct one’s self” (Johnson’s 1824 dictionary). Emma dismisses the idea Jane is diffident but I think she may be wrong to do so. Jane has reason to distrust Emma’s unusual attentions to her and I think Emma is unreasonable to expect her confidence. Mr. Knightley tells Emma “you will soon overcome all that part of her reserve which ought to be overcome, all that has its foundation in diffidence” (21). In other words Jane will soon learn to trust Emma’s overtures to be real and lasting. (Little does he know!) Mr. Knightley also says Jane’s reserve that arises from “discretion must be honoured” (21) suggesting he heard Emma’s questions and Jane answers and thought the later was justified in her discretion. If Jane’s discretion was justified then it seems Emma’s questions could be considered impertinent perhaps due to subject or the degree of their acquaintance or both.