In the RH7 code, the space is part of the 'page' span tag, while in the RH9 code it is part of the 'worklist' span tag.
<span class=SecondaryLink>(space here)page</span>
<span class="SecondaryLink" style="font-weight: bold;">Worklist(space here)</span>
I don't know why it would have changed, but it explains the underline you're seeing.
As for a fix, it might be possible to do a search and replace. I'm unsure if Find: ' </span>' Replace: '</span>' would be suitable. You'd have to some testing to make sure it didn't replace occurrences of space-span that shouldn't be changed. Or if you have someone good with regular expressions they might be able to figure out a good search formula, and use and a tool that will search across multiple text files (not the one bundled with RH, unless it's greatly improved in RH9, which I don't remember seeing mentioned as a feature). FAR (helpware.net) can do that I believe or TextCrawler or you might already have a tool in-house.
The underscore you are seeing is not an underscore, but a style applied by the hyperlink. Hyperlinks are underlined by default and afaik, you cannot overrule the underline of a hyperlink in spans nested inside the list.
The text-decoration you provided in the style sheet stops the span elements to be underlined, but the hyperlink itself is still underlined. If you want to stop that, you need to amend the style of the hyperlink.
About the quotes: RoboHelp 9 uses XHTML, which has a much stricter syntax than the HTML used in RoboHelp 7. In XHTML all attribute values need to be enclosed in quotes. This has nothing to do with the styling.