Can anyone give me any advise on why my store has a index.php ending to the store url? I have never seen this before and i am sure it cannot work for search engines. Even the admin url has a .php ending which i find very strange.

Depending on your .htaccess file, generally your site should not be showing the /index.php in the address bar.

Things to check might be:

1) redirects are enabled for your web server (apache or nginx).

2) SEO addon is installed and active

3) .htaccess file exists and is standard

This assumes that you are entering https://foo.cominto the address bar of your browser and it's changing to

Admin will always show [admin_index_file].php given that no SEO is performed in the admin area.