To verify if your CDN is working properly, look at the source code of your page. If all the CSS, JS, and image linkes say https://yourcdn.com/thefile instead of https://yourwebsite.com/thefile then your CDN is most likely working properly
You must setup a cookieless domain in order for the notification in Pagespeed to go away.
https://www.ravelrumba.com/blog/static-cookieless-domain/
https://www.riyaz.net/blog/how-to-setup-your-own-cdn-in-30-minutes/technology/890/
Your CDN will not show up in Yslow unless you add it to Firefox.
HOW DO I ADD MY CDN HOSTNAME TO YSLOW FOR RULE 2?
Rule 2 says to use a content delivery network (CDN). The score for this rule is computed by checking the hostname of each component against the list of known CDNs. Unfortunately, the list of “known CDNs” are the ones used by Yahoo!. Most likely these are not relevant to your web site, except for potentially yui.yahooapis.com. If you want an accurate score for your web site, you can add your CDN hostnames to YSlow using Firefox’s preferences. Here are the steps to follow:
Go to about:config in Firefox. You’ll see the current list of preferences.
Right-click in the window and choose New and String to create a new string preference.
Enter extensions.yslow.cdnHostnames for the preference name.
For the string value, enter the hostname of your CDN, for example, mycdn.com.
Restart Firefox.
Do not use quotes. If you have multiple CDN hostnames, separate them with commas.
If you specify CDN hostnames in your preferences, they’ll be shown under the details for Rule 2 in the Performance view.