I want to help others on Stack Overflow. I've set a watched tag. Is it possible to be notified about new questions with this tag to a special e-mail address?
If I understand correctly, the main issue is that you want to specify an email address - which might be different from the address you have currently in your email settings.
As far as I can tell, if you use tag filters, you can choose an arbitrary email address which you want to use for notifications.
If you go to https://stackexchange.com/filters/, you can set-up a filter for a specific tag on one site or multiple sites. And you can choose whether you want to receive an email with new questions too - the options are once per day, every 3 hours or every 15 minutes.
As a test, I have just tried to use a filter for the tag discussion on all sites. And as a test, I have set it up for "every 15 minutes". (I wanted to use something with relatively high volume of questions - so that if it works, then I receive some notification relatively soon. I suppose that the tag discussion over all meta sites fulfills this requirement.)
So far I have received an email asking to confirm my subscription. I did that, and I'll report later whether the test worked.
An a few hour later, I can confirm that I received several emails with new question on the email address that I entered.
You can manage your subscriptions not only through the page with filters, but also in the subscriptions tab of your network profile. This is described in the answer here: How do I get notified about a new question in my favorite tag? (The first part of the answer is something that works differently - instead of subscribe/unsubscribe you now get watch/unwatch tag. But possibility to manage your subscription in your network profile seems to work in the same way as back then - judging by the screenshot.)