The results may be almost instantaneous(or in 1 or 2 days). You'll rank high in Search results ..but the links should be related to your niche..and 1 or 2 links didn't make such a huge difference.
Yes You R Right But Some Time Google is Depend on Your Site. Your Site is Old and Very popular So Google is Fast Priority To You.
Your PR rank updates every 3-4 months but as far as results in search engines it does only take 2-3 days at most sometimes maybe a week.
This would be a toolbar export (or 'public' PR). Actual (internal) PR is ever-changing, otherwise it would make that variable within the algorithm next to worthless. As soon as G finds your links, it is taken into consideration. This would depend on the source of the link, and the frequency at which Google crawls that site.
If you're talking about PR changes - you will see them on the next PageRank update. However SERP changes might occur in just a few weeks
The results will become better and better with time, at start you will gain a bit, and as time passes by you'll get more and more, based even of the age of the backlinks. So don't look at it as a "how fast" but see it as a "long time investment.
If you are looking for a way to get one way relevent backlinks with PR, try neurolinker which was released a few days ago. I was one of the testers and it does what it says on the tin!
Google updates its pr all the time but only update the external pr every couple months. If you had good links with good anchor text, it could happen over night