Q: invoiced for purchase I didn't approve

What 'form' did you fill in ? It's likely to have been a phishing email trying to get your account and payment details and not from Apple.

Phishing and similar emails : Phishing & Other Suspicious Emails

Phishing emails : Identifying fraudulent "phishing" email - Apple Support

Genuine iTunes emails : Identifying legitimate emails from the iTunes Store - Apple Support

Viewing your account's purchase history : See your purchase history in the iTunes Store - Apple Support

If it's a genuine email and it shows on your account's purchase history, and nobody else has access to your account or devices/computers, then contact iTunes Support : https://support.apple.com/contact . And change your account's password http://appleid.apple.com (is that how you've already changed it ?) - after changing it : What to do after you change your Apple ID email address or password - Apple Support.

If it is a phishing email you could forward it to Apple : reportphishing@apple.com , and then delete it.

This invoice that you received, did you check your purchases in your iTunes account to see if that was an actual purchase, or did you check your bank account to see if there was an actual charge?

It is very possible the invoice that you received was a phishing attempt to get your account information. Did you click on any links in this invoice to add/remove/change any of your account info? If you did that, then you may have provided the information to compromise your account. If you did not do that, and made changes to your account via iTunes individually, then you should not have a problem. However, changes to your passcode in iTunes triggers a number of other things that have to be looked at. See this support document for that info. What to do after you change your Apple ID email address or password - Apple Support

I'm glad I was able to help. Don't feel stupid. These people are very good at what they do, that is how they make their money, etc.. So long as it is a learning lesson, then it isn't all in vain. Take care and good luck.