no need. most of all other search engines follow google, yahoo and MSN. they will chatch yout site autamatically. Open directoy is best option to get great backlinks.
Submit your new site to SE like what you have posted above.. then explore your link building, if you are new to SEO better read this seobook.com to learn more.
Just build links for your your website and should be on theme and relevant. No need to submit into all search engines
Well if you really want to do search engine submissions then the ones that you mentioned should suffice. Personally I would suggest to abstain from wasting your time doing it. Search engines will find you, they are good at doing it. Get links from some high traffic websites and your job is done.
What is need is having your links placed on a dofollow high traffic websites and is crawled regularly. Most of the time blog commenting will do and that will help your site getting indexed fast if it's a newly setup site.
If the site is new and you want it to be indexed quicker than yes, but if you take your time and add links than it will happen on its own.
Well there is no need to submit your site in any of the search engines. Search engine spiders will automatically crawl your site and will index the website. But make sure your site is optimized with proper keyword placement in the title and description, within the body content. Submit your site in the popular social bookmarking sites and you will soon find your site indexed. Thanks
Although you don't need to submit your site, if you do, do it only once to Google, MSN and Yahoo. After that, just do link building.