she really asked, we can invent our own :)

"She seemed bent on giving no real insight into Mr. Dixon's character, or her own value for his company, or opinion of the suitableness of the match."
This is only the gist of what she wanted to know. The questions needn't be direct.

Knowing 'character' could mean anything.
I'm not expecting Emma to ask;
'Is he a good charactered man? Does he flirt with other women?'

She may have asked.

'Is he fun loving. Enjoys sport, parties, music and does his wife enjoy it as much. Will they be able to do all that in Ireland. Did one have good conversation with him.' or something like that.

Neither must Emma have asked;
'Did you enjoy his company?'
She must have asked.
'Could one have good conversation with him or was he shy and reserved in the company of other people except the family and perhaps you?'

This can also tell about ones character.

It reminds me of Marianne asking Sir John in S&S about Willoughby's character.

So stonewalling your hostess for asking such normal questions is downright rude IMO.

Especially when all what she writes is already known to the whole of Highbury, and Jane cannot be ignorant of that.