I am asked to install Outlook. Is it necessary ?

No, you don't need to install Outlook to use BirdieSync.
Did you select "contacts, calendar, tasks or e-mails" categories in ActiveSync/Windows Mobile Device Center options ? If yes, these are Outlook categories. If you want to synchronize with Thunderbird or Sunbird, you must select "card, events, tasks or mails" in ActiveSync/Windows Mobile Device Center options.