To be clear: 1. Page Rank is a part of Google's brands, so you can't talk about it and refer to Yahoo! 2. Page Rank does not affect your ranking position directly. It used to, some time ago but they have changed their algorithm. And regarding your questions, there is mainly the same criteria. It's just that Google has lot more activity than Yahoo!. Also, lots of developers don't consider Yahoo's rules when making a SEO campaign, since the best search engine (and the one to bring you most of the traffic) is Google.
There's no page rank in Yahoo, if you want to rank high in Yahoo results do the same thing as in google i.e. build links.
Page rank is the Asset of Google. No any other search engine can use this toolbar. If you want to increase the ranking in yahoo. update your content, do good on-page of site, generates as many as backlinks but good no spamming for site.