After i run “mailbfr -f” to fix my cyrus database, all mail shows up as unread.

Unfortunately we haven’t found a safe way around this issue yet. You’ll have to live with it. Important: "mailbfr -f" should only be used if your database is corrupted, not just for the sake of it and not just to recover a single user. If you need to fix a single user, issue "mailbfr -m username".

Should I use full, incremental or rotate for backups?

There are pros and cons for each method. Again this really depends on the amount of mail and mailboxes you have.

Although we cannot decide for you, we favor “rotation”. Rotation will make a full backup per week and just add changes on a daily basis.

mailbfr thinks the path I have given is not correct?

Most likely your path contains spaces. This is generally not advisable. If you cannot take the spaces out of your path for some reason, you will need to "escape" them.

I restored my mail server. Now I see messages/mailboxes that were deleted?

mailbfr does an incremental backup by default. So unless you change the backup location regularly you may end up with old messages. This is by design otherwise you couldn’t go back to an old messsage a user might request. If you do not wish this behavior, use the "full" or "rotate" option.