Hello,
Regarding the Homepage synchronization between devices, this is a known Firefox bug that I reported some time ago:
https://bugzilla.mozilla.org/show_bug.cgi?id=1412083

What should help is excluding Homepage from synchronization:
https://support.mozilla.org/en-US/questions/919674
(basically just set in "about:config" page setting "services.sync.prefs.sync.browser.startup.homepage" to false)

Regarding drag and drop - you probably activated the "Super-speed" feature (in upper right menu). When this feature is enabled, you can drag and drop only when holding Ctrl or Shift keys. You can also disable Super-speed.
I hope this helps :)

Best regards,
Juraj Mäsiar