is there any limit to submit my new website to directory submission sites? or it depends to on how many? I have a list of 300 directory submission sites, is it okay if I will submit my site in all 300 for 1 week?
It depends on directories. Usually it takes up to 6 months to get approved, so it doesn't matter will you submit all your links in a week or in a day. Back links appearance will be distributed in months. But it is true only for free submission. If you pay, your links will be approved in a week or two.
It doesn't matter, but according to the latest google penguin update and its impact, Google now gives priority to the human approval submissions, not instant approval.