No. Google can't know that you submitted to 2000 directories in a day (nearly impossible if you are doing it manually anyway). Directories take a long time to approve the links and Google (and other bots) have to reindex their category pages to find new links.. Even if google hated this practice it won't be easy for them to detect.
no they dont. in fact, when they crafted their webmaster guideline initially, they suggested webmasters that they submit their sites to link directories. these days there are thousands of directories and lot of them are worthless, but if you submit to good list of directories, it is still a safe link building practice.
I have hired a person once to submit one of my websites to 10.000 directories. It didn't harm at all, the website turned out just PR2 tho and a year later only 2400 backlinks remained because the person submitted to loads of .INFO directories.
It won't hurt unless that is the only kind of links you have. If you get 7,000 links and all are from directors and nothing else, Google does find that fishy. You need links from different sources as well.
It largely depends on the quality of the directories you're submitting too. If you're submitting to that many I would hazard a guess that they're low quality and won't offer much benefit anyway.
I can't imagine that it would. Google themselves have always recommended that new webmasters especially, submit their site to directories as one way to build links. They never said, "...but not TOO many directories." They even used to have their own directory at one time I think. Many years ago now.