US dollar dropdown is not all from that section, which also contain tax and language selectors. The best, if you will open View/Shared/_Header.cshtml file and check how it is build. Also you may do change there, by moving Logo component in a place of currency.
Please note, do not modify original files! Copy that file to your new theme (or move it to default clean folder).
There is no hr tag below, but it is css border style...
As see, you would like to made some customization of nopCommerce. I recommend to read
this documentation first.
Regards,
Tom