Intermittent sends are obviously more difficult to pin down. WordPress has pretty notorious hit and miss email sending but it is usually clear one way or the other. and I can only really help with SP emails as they are the ones I know. So – some things…
Forum admins do not need to use the subscriptions as they can turn on email notifications on the forum admin > Your Admin Options. Unless they do not want ALL notifications of course.
The email address you have set up in the WP Settings > General is the one that will be used for sending and it does need to have a valid email server behind it. In other words it must be genuinely capable of send out emails.
By default, WP sends all emails as being sent by ‘WordPress’ which most people do not like. The forum admin > Options > Email Settings panel allows you to override this with your own email name etc. Ensure these settings are correct.
Finally, a lot of people – including us as it happens – have problems with WP mail. There are a few plugins in the repository that may help with this. The one we use is called ‘HGK SMTP’ and we have recommended it to many users over the years with near universal success I believe.