I just want to know what impact would you have on other pages of the site if you have a first page ranking for a term like shoes. How much link juice will it give the other pages on the site say for the term "ladies shoes". I have seen sites (their home page) ranking very high for terms like shoes but also for ladies shoes, but even though when you check the back links its focused largely on "shoes"
Link juice will depend on the number of links in the page. Many links minus link juice. But a link from a page that is an authority in "shoes" will be high valued if the linked page has shoes as a keyword. Unfortunately the exact measure of importance only google knows.
As long as you have optimised your site pages well then I should see no problem in the long term/future your site gaining favourable position in Google for those pages. Also, it could lead to having authority links show up when users search your keywords.
Link juice is something different and probably not the right term to use it here. - The site is ranking well for shoe/s because it is externally links in a massive number or term "shoe". Internal pages rank well on term ladies shoe because that page has massive internal links from home page and other category pages which are with high PR and authoritative page by itself.
ranking for shoes will definitely have a great impact on related terms too, if Google trust you enough to give you top rankings for "shoes" it means your website is an authority site and a respectable source in the "shoes" niche, hence, it is only natural to have great rankings for "ladies shoes", "boy shoes", "sport shoes", "walking shoes" because they are all sub categories of "shoes".