Sitemap is a xml file which contain full list of your website urls. It is used to include directories of your websites for crawling and indexing for search engine and access for users. it can help search engine robots for indexing your website more fast and deeply. It is roughly an opposite of robots.txt You can create a sitemap.xml by various free and paid service or you can write it with proper way (read about how write a sitemap).

Also keep these things in mind:
1) Sitemap must be less than 10 MB (10,485,760 bytes) and can contain maximum 50,000 urls. if you have more uls than this create multiple sitemap files and use a sitemap index file.
2) Put your sitemap in website root directory and add the url of your sitemap in robots.txt.
3) sitemap.xml can be compressed using grip for faster loading.

Broken link: a broken link is an inaccessible link or url of a website. a higher rate of broken links have a negative effect on search engine ranking due to reduced link equity. it also has a bad impact on user experience. There are several reasons for broken link. All are listed below.
1) An incorrect link entered by you.
2) The destination website removed the linked web page given by you. (A common 404 error).
3) The destination website is irreversibly moved or not exists anymore. (Changing domain or site blocked or dysfunctional).
4) User may behind some firewall or alike software or security mechanism that is blocking the access to the destination website.
5) You have provided a link to a site that is blocked by firewall or alike software for outside access.
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doc type is not SEO factor but it is checked for validating your web page. So set a doctype at your html page.
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Older HTML tags and attributes that have been superseded by other more functional or flexible alternatives (whether as HTML or as CSS ) are declared as deprecated in HTML4 by the W3C - the consortium that sets the HTML standards. Browsers should continue to support deprecated tags and attributes, but eventually these tags are likely to become obsolete and so future support cannot be guaranteed.

HTML page size is the one of the main factors of webpage loading time. It should be less than 100 KB according to google recommendation. Note that, this size not including external css, js or images files. So small page size less loading time.

To reduce your page size do this steps
1) Move all your css and js code to external file.
2) make sure your text content be on top of the page so that it can displayed before full page loading.
3) Reduce or compress all the image, flash media file etc. will be better if these files are less than 100 KB
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GZIP is a generic compressor that can be applied to any stream of bytes: under the hood it remembers some of the previously seen content and attempts to find and replace duplicate data fragments in an efficient way - for the curious, great low-level explanation of GZIP. However, in practice, GZIP performs best on text-based content, often achieving compression rates of as high as 70-90% for larger files, whereas running GZIP on assets that are already compressed via alternative algorithms (e.g. most image formats) yields little to no improvement. It is also recommended that, GZIP compressed size should be <=33 KB

Internal css is the css codes which resides on html page inside style tag. Internal css is increases loading time since no page caching is possible for internal css. Try to put your css code in external file.