I think Darcy probably is jealous that Fitzwilliam can converse so easily with Lizzy when he has very little sucess himself. But given he knows his cousin's financial situation, he knows the Col. cannot afford to marry her, so the only impact it could have on Darcy is in seeing the lady of his interest apreciated by someone of good judgement. As it is not her character that he objects to, this probably would not have spurred him on.

] Also, do you think, if he had been financially independent, Col. Fitzwilliam would have made an offer to Lizzy? He doesn't seem to mind her low connections. Would she have accepted?

I think in chapter 33 he's trying to tell her he would have.
"I speak feelingly. A younger son, you know, must be inured to self-denial and dependence....I have experienced many hardships of that nature. But in matters of greater weight, I may suffer from the want of money. Younger sons cannot marry where they like."
As for Lizzy, I am no sure whether she would have accepted or not. She doesn't seem to be expecting his attentions " 'Is this,' thought Elizabeth, 'meant for me?' and she coloured at the idea" so given her approach to marriage, possibly not. However, she does seem quite ready to be fallen in love with - she is quickly apreciative of Wickham, although that could be based on a common dislike of Darcy. Upon meeting the reformed Mr Darcy, she rapidly comes to desire his good opinion, and we should not attribute that to his fine estate. So perhaps in a differenct situation - and the absence of a Darcy - if Fitzwilliam had been able to persue an interest she might have eventually accepted. But she does not seem as apreciative of him as he is of her, she is just being her lively self. Hard to know.