Hi, I think this is what you are asking for : https://support.mozilla.org/en-US/kb/customize-new-tab-page

You can use this add-on to do many things : https://addons.mozilla.org/en-US/firefox/addon/new-tab-override/

Please let us know if this solved your issue or if need further assistance.

You can update to Firefox 59 to be able to rearrange the tiles more easily.

• Help -> About Firefox
• https://support.mozilla.org/en-US/kb/update-firefox-latest-version

Completely different issue :

Your system details show 'Search Extension by Ask', which you probably didn't install yourself, as it is a browser hijacker.

Go to the Firefox menu (≡) => Add-ons => Extensions and look for any unfamiliar or suspicious looking extensions.

When you find any : remove them.

Do the same in Windows Control Panel => All Programs

However : most malware will be 'hiding' somewhere , so let's run malware scans (even though you already have run some) :

Further information can be found in this article : https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware?cache=no

Run most or all of the listed malware scanners. They all work differently - what one program doesn't pick up, the other might.

Also see : https://malwaretips.com/blogs/remove-search-extension-by-ask/