Are the files in iCloud Drive also local on my Mac so I can access them when I do not have an Internet connection - which is common and I need offline access to my files.

iCloud Drive does in fact keep a local copy of all files placed there, so you should be able to open and work on files in iCloud drive even when you have no internet access.

It will depend on your version of OS X and your System Preferences for iCloud > iCloud Drive.

• With Yosemite and El Capitan all iCloud Drive files will have local shadow copies for offline working.
• With macOS Sierra you have a choice. If you enable "Optimize Mac Storage" in the options for iCloud Drive in the System Preferences, the files you did not use in a long time may be removed from your Mac and only stored on iCloud Drive, if you are running out of storage on your Mac. Then you will need an internet connection to work with the iCloud Drive files you did not use in a long time.