What changes to the game will the "On The Brink" Pandemic expansion offer me?
To answer all your questions, but not in order:

Other things you should know:  Also adds some rather nice storage trays for the viruses, and some smaller pawns (including for the original base roles) which fit on the board better.  All of this stuff will just fit in the original box, but only if you're good at packing (the virus trays could actually do to be about 10% smaller).

The new roles add significant variation to the base game even without using any of the other new mechanics in the set.  (There's also a reprinted Operations Expert card with revised wording, which I recommend also using for the base game.)  It becomes tempting to add house rules for how you select powers; there's one new power that's related to (but a major variation on) each of the original roles, and some completely unrelated new roles on top.  This means that purely random draw can, if you're unlucky, produce some very odd or tricky mixes.  (Some groups, of course, prefer it that way.)

The expansion makes the game last longer only if you're using the new disease variants.  The bioterrorist option in particular takes longer, as it adds a hunt-the-hidden-player mechanic (a little bit like Fury of Dracula).  Mutating diseases add a little more complexity and hence a few minutes more playtime.  (They also make it harder, so they can dramatically shorten the playtime...)

Most of the variations on disease - and hence a lot of the set content - make the game more difficult. So if you regularly find Pandemic challenging, consider carefully: you might have trouble using some of the material without making it too challenging.

The question you linked addresses 6-7 players better than I can here. Short form: it works, but not at all well unless you add house rules to cope with the massive difficulty increase.  (Personally, I'd always rather play something else with 6 or 7; Pandemic really wasn't designed for it.)

Summary:

(Personal opinion: I found it to be fun, but expensive for the amount of content.)

Does it add enough that it's worth getting instead of an entirely new game?  Depends how much you play Pandemic.  If you play intermittently or are still finding the base game surprising you, probably not; use the revised Ops Expert wording and get another small game instead.  If you play Pandemic regularly and feel like you've seen all the base game has to offer, it's definitely worth getting.  If you regularly beat the pants off Pandemic and want some more challenging options, grab it.