Amazon Fire TV Stick Netflix Free?

My mom really wants to have Netflix. Unfortunately this is apparently not possible with a normal television set or with your receiver. That's why I thought about getting an Amazon Fire TV Stick with which this should work. We already have a Netflix account, but my question is now,

If she wants to watch Netflix on the stick, does she have to pay an extra subscription for the Fire TV Stick in addition to the Netflix subscription?

or do you just plug it in and start using Netflix without covering other costs?

The Netflix subscription is extra.

Yes, that's clear, but do I pay a subscription to use the stick myself?

You pay for the stick once), then the Prime subscription on Amazon for the Amazon content and then the app use on Netflix.