You can copy the places.sqlite file to the new profile to get the bookmarks and the history and cookies.sqlite for the cookies.
There are also JSON backups (bookmarks-####-##-##_xx.json) in the bookmarkbackups folder that can be used to restore the bookmarks.
You may also want to copy the permissions.sqlite file for the allow/block cookie exceptions and other exceptions.
You can use this button to go to the Firefox profile folder:
Help > Troubleshooting Information > Profile Directory: Show Folder (Linux: Open Directory; Mac: Show in Finder)
For more info: http://kb.mozillazine.org/Profile_folder_-_Firefox
I hope it will helpful for you to resolve your problems.
Thanks & Regards