I'd have to have a closer look at the text (or be more familiar with 19th-century American literature than I am) to say for sure, but I don't think the subjunctive here indicates any extra meaning. Re: your first question, I think that 'should she win it' is a good gloss of 'if she win it'. So please know that my answers might well be different if I were. I should start off by saying that I'm not familiar with this text or the context in which the sentences you ask about occur. I am not sure how 'lack of' can work in this case. Does he mean 'in addition to that the validity of the moral point we gather from Hutchinson's character allows for an introduction here'? I interpreted 'want for' to mean 'preference for', not as 'lack of'. I am not sure what the author means by the second half of this sentence (after 'besides'). 'The character of this female suggests a train of thoughts which will form as natural an introduction to her story as most of the prefaces to Gay's Fables or the tales of Prior, besides that the general soundness of the moral may excuse any want to present applicability'. The other question is from the same document, but comes from the opening statement. Isn't he saying 'I don't think women can win it'. Therefore, is it correct to conclude that Hawthorne in using the subjunctive mode is expressing a disparaging view about a woman's potential. The author writes, 'Is the prize worth her having if she win it ?' I understand 'if she win it' to mean 'should she win it', which in turn means that the author has doubts about 'her winning it'. My first question is about the meaning of a question appears in the subjunctive mode in the text. The text is 'Mrs Hutchinson' by Nathaniel Hawthorne. Hello, I have more questions about texts from the 19th century.

Modal verb exercise