A fresh upload will always have files 644 and directories 755, so that's completely normal; you have to re-chmod things at their new location.
"officially" all UBB directories (now don't go chmodding everything you uploaded that has nothing to do with the UBB lol) should be 777 and files in them 666; this is so they can be updated by the software and it was just "easier" to give a broad scope.
The forum directory itself (that holds the UBB files) should be 755.
As for the last part about accessing header.php; on my site I have all of my little files to be included on every page load in a directory called includes/ and this directory is set to be forbidden from access (a php include will still be able to load the content) then no one can access the files (but really, who's going to KNOW they're actually there)
