i have never submitted my site to search engine for indexing, however i am contemplating doing so especially with yahoo and bing. this is because i realized my site can be found by google but not by yahoo or bing.
Yes, I always keep my sitemap updated in the search engines. Especially for Google, I always make a sitemap regularly and submit it. This makes all of my pages properly indexed in search engines. I also sue Google Webmaster Tools for checking errors in my website while indexing. There are many useful tools in Google Webmaster Tool that can be used for keeping track of websites ranking.
Site submission to search engine is unnecessary. Because whether you submit or not, your site will be indexed on search engine automatically. However it takes time. Submission is just to speed up the process.