If I have a root folder with some restrictive permission, let's say 600, and if the child folders/files have 777 permission will everybody be able to read/write/execute the child file even though the root folder has 600?
The precise rule is: you can traverse a directory if and only if you have execute permission on it.
So for example to access
dir/subdir/file, you need execute permission on
dir/subdir, plus the permissions on
file for the type of access you want. Getting into corner cases, I'm not sure whether it's universal that you need execute permission on the current directory to access a file through a relative path (you do on Linux).
The way you access a file matters. For example, if you have execute permissions on
/foo/bar but not on
/foo, but your current directory is
/foo/bar, you can access files in
/foo/bar through a relative path but not through an absolute path. You can't change to
/foo/bar in this scenario; a more privileged process has presumably done
cd /foo/bar before going unprivileged. If a file has multiple hard links, the path you use to access it determines your access constraints.
Symbolic links change nothing. The kernel uses the access rights of the calling process to traverse them. For example, if
sym is a symbolic link to the directory
dir, you need execute permission on
dir to access
sym/foo. The permissions on the symlink itself may or may not matter depending on the OS and filesystem (some respect them, some ignore them).
Removing execute permission from the root directory effectively restricts a user to a part of the directory tree (which a more privileged process must change into). This requires access control lists to be any use. For example, if
/home are off-limits to
setfacl -m user:joe:0 / /home) and
joe's home directory, then
joe won't be able to access the rest of the system (including running shell scripts with
/bin/sh or dynamically linked binaries that need to access
/lib, so you'd need to go deeper for practical use, e.g.
setfacl -m user:joe:0 /*; setfacl -d user:joe /bin /lib).
Read permission on a directory gives the right to enumerate the entries. Giving execute permission without giving read permission is occasionally useful: the names of entries serve as passwords to access them. I can't think of any use in giving read or write permission to a directory without execute permission.