How do I know a specified user's permissions on Linux with root access?

It may be the case that your colleague, while creating the account, created the home directory "by hand" which resulted in it being owned by root. Try running the following as root:

chown -R username ~username
chgrp -R $(id -gn username) ~username

Where username is the name of the problematic account.

Edit

If this turns out to be your problem, to avoid this happening in the future, you want to add the -m switch to the useradd command line used to create the user account. This ensures that the user's selected home directory is created if it doesn't exist. This creates the home directory with the "right" ownership and permissions so you don't face this kind of issue.

Edit 2

The chgrp command added above will change group ownership of the entire home directory of username to username's primary group. Depending on your environment, this may not be exactly what you want and you'll possibly need to change group ownership of specific sub-directories inside the home-directory "manually", thereby setting different group ownership for different sub-directories. This is usually not the case for personal computers, but since you mentioned "a colleague", I'm assuming we're talking about a networked office environment, in which case group ownership is important for shared directories.