A good option to have a sitemap but not actually required. This will help you to monitor some section of your sites (for some section like index pages, IBLs, top search queries etc...) like on Google. Sitemap has nothing to do with your SERPs enhancement.
Exactly, I don't want Google to index all the links on my site, so contrary to the popular belief, I don't like to generate sitemaps on my sites.
It doesn't make any difference at all. It obviously makes Googles job easier though which is why they are keen to promote its use to webmasters.
It helps speed up the process of Google bots crawling your website when information is updated on your website and allows for each page to be indexed quicker.
We should submit sitemap but it is not necessary if a website is small or if google easily crawl all the pages. It doesnot help in seo. A sitemap just information search engines about the pages of a website so that it can crawl easily by search engines.