Hello,
I've submitted
http://www.koycegizdamla.com/sitemap.xml to Google and it reported no errors (sitemap is valid).
Also can you let me know where the "special page" is so I can sort out my bad links?
The broken links are detected by the application and reported on the special page, providing also the URLs pages that refer to these bad links.
You should modify the "source" pages of your site reported in that list - find the "target" link (which is broken) and correct it.
Another question, do I have to upload my website with the new map on to my computer before working on changes to the site?
There is no need to download sitemap to your local computer - it should be updated on your host only.