Rather than logging in to root - if you really want a proper root session then I suggest you instead run an interactive sudo session
This won't help with your drag-and-drop problem though. You would instead need to run the file manager as root
Even if you try to "ignore" the security features of Linux they are likely to cause problems in future when you wonder why your webserver application can't read the directory that only root can access etc. - so far better to learn it properly.
To set the permissions correctly you should use chown and chmod to set the permissions.
For example if you'd like pi to own the /var/www directory then you would use:
To make sure everyone can read the directory
u = user (owner of the file / directory)
g = group
o = others (all other users)
r = read access
w = write access
x = execute permission (on a directory allows you to change to that directory)
So that everyone can write to the directory (not required normally, but helps remove the security barrier)
To take access away use - instead of +
You can also change the permissions of files and sub-directories using File manager - right click on a file or directory - choose properties and then the permissions tab. If you need to change permissions to files or directories that you don't own then that has to be done using root - either on the command line using sudo or through file manager started with gksudo.
I have created a tutorial on Linux file permissions