I believe that if you have multiple links from a web site to the same page of your site Google will count 1 of the links and ignore the rest.
there is no defined limit on the number of directory submissions you are allowed to do per day each directory is individual and the directory owner will be different in most cases directory submission is a time consuming process and you never know whether your link is going to be approved/rejected by the directory owner being realistic, you can submit anywhere to 20-30 directories on a daily basis, make sure that the directories you are submitting to has good PR and belongs to your sites niche for best advantage