What's the difference between {vb:raw session.sessionurl} and {session.sessionurl_q}
 

I noticed some of my nav tabs use one and some use the other

I think all your tabs should use {session.sessionurl_q}. In a template you would use {vb:raw session.sessionurl_q}

How can I put a phrase in a nav tab's text?

If you mean the title, I don't know if you can put a phrase in it, but when you create a tab it creates a phrase for the title. When you edit a tab, at the top there's an "Identity" value. If you search for that in "Search for Phrases" (with "Phrase Variable Name Only" selected and "Exact Match" set to no) then you'll find the phrase and you can enter a translation.

I really don't know what to do here... (although this is mostly a different question the the original post)

Before 4.2, I had a hook in the title of a custom tab I made with a template. I can't put a hook in a phrase, right? And if I make the tab in a template like before, I can only put it before or after the manager's tabs instead of a specified display order?