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if your website's internal linking is correct and does not have deep pages, Google will automatically find the page. However if you are using WordPress, you may use sitemap generating plugins; like "WordPress SEO" by Yoast.
No need to submit your sitemap repeated.
I believe Google shows based on local SEO. However if you are searching mobile, obviously it can track your location.
Interestingly, it also track when you are logged in on desktop and your mobile is providing the location data.
I would advice you to read this blog post https://moz.com/blog/how-to-have-a-successful-local-seo-campaign-in-2015 and follow this section https://moz.com/ugc/category/local-seo
Wish you all the best.