1) In order to have access to a file/directory, do you have to have permissions to all the parent directories down to the root directory? Or can you access a directory if you do not have permissions on the parent directory?
Let's say if the user doesn't have read-permission to
some or all of the directories in the tree but has access
to a single file s/he has to specify the fully qualified name
of the file to access it.
2) Do all new files and directories take their permissions from their parent directory?
Nope, they take it from umask. Do a man umask for
3) Is there a way to change default permissions when directories and files are created in a specific place?
Yes, usually you'll want to modify umask for that.
To do it temporarily you can use the utility umask,
if you want it changed permanently (bad idea, the
default is very sensible!) edit /etc/profile and go
for umask there :)
For a good overview go here