1) To remove sign up and sign in links edit your default.xml code at below location.
Add these lines of code
<referenceBlock name="register-link" remove="true" /> <!--for sign up Link-->
<referenceBlock name="authorization-link" remove="true" /> <!--for Sign In Link -->
2) Add more links with account links enable this block Custom Top Links (to replace Magento's default Top Links)
Go to Admin > Content > Blocks > Custom Top Links (to replace Magento's default Top Links) > Enable
Place your custom links in this block
3) Add custom links in main menu with Home these links come at right side by defaul
Go to Blocks and edit this block "Main menu - custom links" add your custom links for main menu here.
see below picture , I put some custom links at both place and removed the links which you wanted to remove
4) Placing custom links next to Home Link
For this you can use this simple method of placing custom links:
All done !
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