its a different phenomenon ... increase in backlinks doesn't reflect any changes in keyword rankings. Number of backlinks keep on changing as you might have got any new backlinks or if you had sitewide links on some websites then your backlinks will increase with increase in pages of linking website.
hmmm Sometimes yes, and sometimes No.... It depends on What quality of backlinks are? Backlinks..... should be from authority websites, if you want your websites to rank high...!
The number of your backlink has no effect in your keyword rankings.. cos the number of backlinks is not constant... Its growing as long as you did something on that.
well, no one has said anything about link anchor yet...if these new backlinks are worthy and have the same link anchor you are looking to rank with, then its just a matter of time
Yeah, depends on whether or not you have relevant anchor text, and it'd help if the website is relevant.
That is almost an impossible question to answer. If the quality of your backlink is good i.e from sites with higher PR then it may have an effect, but it's impossible to say for sure.