No headers in some folders
Some folders do not show the message headers, just a blank space. I can click on the space where the headers should be and can see the message in the lower panel, so the messages are there.
Alla svar (1)
It looks like your mail files are corrupted. First of all create a backup of your Thunderbird profile folder. https://support.mozilla.org/kb/profiles-tb#w_backing-up-a-profile
Then try to rebuild the index file of the troubled folder. Right-click the folder - Properties - Repair Folder
Note: depending on the corruption this may erase messages from the affected folder which cannot be recovered anymore. In that case you'd need to restore them from a recent backup done prior to the corruption.
Corruption is often caused by anti-virus software messing with Thunderbird mail files. It is therefore recommended to create an exception for the Thunderbird profile folder, so that the real-time scanner won't attempt to scan the profile with your mail.
For more information on the profile location see http://kb.mozillazine.org/Profile_folder_-_Thunderbird
Also see http://kb.mozillazine.org/Keep_it_working_-_Thunderbird