User Template refuses my access.

The User Templates folder contains the template for new users. When you create a new user account, these files are copied into your account. It contains the library, movie, music, pictures, and documents folders, for example. You should not edit this folder. Because you are an admin user, you could unlock it if you wanted to, but the system has locked it for a very good reason. It is normal that it is locked.

If you are just curious about the contents of the folder, you can copy it to the Desktop with an option-drag. The pointer will show a green circle with a plus sign in it as is normal for a drag copy, but when you release the mouse button, you will be asked to confirm that you wish to 'move' the item & asked for an admin name & password if you do. Do that & a copy of the folder will be created on your Desktop that is owned by you.

You can examine this copy to get an idea of what the template contains without fear of damaging the original, which is owned by system (a.k.a. the root user).

That folder, and many more, belong to the system. As already noted, don't muck with things at the root-level, such as System and Library, unless you know exactly what you're doing. If you insist, then you need to enable the root user account, but I don't recommend doing that. I've never enabled it in the six years i've been running OS X. It's a last-ditch maneuver. Alternatively, you can use to Terminal app and the sudo command to get information on those items.