I just created a sitemap for my new website. And used webmaster tools trying to optimize my site for the search engine. Are these services free? In other words, which ones are free and which are not from google webmaster tools?
It's free, Google Webmasters tools are for free! You just have to submit your created sitemap in order for Google to index your website.
Wrong. There is NO requirement saying that you NEED a sitemap to be indexed. Google et alia will index most sites just fine WITHOUT a sitemap. HOWEVER, for some sites, a sitemap is mandatory else the bots cannot find the pages. That said, a sitemap SHOULD be included on ALL sites that have numerous pages. Creating a sitemap for a website with fewer than 100 pages is usually a waste of time. I did not add a sitemap to my website until I had 9,000 pages and Google indexed it just fine WITHOUT a sitemap for YEARS.
Both Google Search Console (SC) and Analytics are free and should be created for all websites. Bing also has their version. By just setting these up, Google will index your site. However, I would create a xml sitemap for it and then submit it to SC's sitemap feature. Also, it you have any other website that Google is indexing, just add you full url to your website, Google will then read it into the index and say- a week later, remove your link. Google will visit your site from then on depending on the changes you are making.