It’s difficult to say what the problem is without more info. It is not uncommon for the email that is sent to the website visitor to not show up (#2 in your original post). However, it is very uncommon for the notification email to not show up (#1 in your original post – the CF7 email).
It’s possible there is something wrong with your hosting account email — I have seen that once before. However, it’s more likely that the From: of the email is causing the problem. That is almost always the issue for the #2 scenario (the one going to the website visitor). It’s not usually the problem for the #1 scenario, but it could be, depending on exactly what you put in the CF7 form.
The reason the From: causes problems so often in the #2 scenario is that on shared-hosting computers, the From: of the email gets set to some account on the shared hosting computer itself (normally this is completely unrelated to your domain or set up). That makes the receiving email system think that it is spam and it blocks it. This is common when the website visitor has a Yahoo email address (and some other providers also do it). EBD does not provide a way to set that From: value without an additional plugin, so that’s why this happens a lot. But, it doesn’t usually happen in the #1 scenario because the CF7 form lets you set the From: value. Normally that is set to something that just works by default, but it’s possible that it might not.
So, typically you want the From: value to be a real email account that exists on your hosting cpanel, not like a gmail account or anything like that (because it will look to the receiving email system like there is some non-gmail.com system connecting to it and trying to give it email with a From: of a gmail address, which looks like it would be spam since they don’t match).
Now, since I can’t really see any of your values or try anything, all of the above is really just speculation based on dealing with lots of these email support issues for the past few months. If I had to guess, I would guess that your hosting provider email account is blocking the incoming email (which is technically coming from one of its own systems) because it thinks it is spam. However, it may just be some sort of misconfiguration somewhere that you need to contact hosting provider to figure out.
There are a couple of things we can try before you get to that point though… First, if you can, add a URL to your EBD page in here so I can go try it and just make sure everything looks ok. Second, you could install a plugin like Postman SMTP, which will provide a log of exactly what is happening when the email goes out. I suggest you tell me the URL to try first, if it’s available on the web, and let me check that first. Then, you can do the plugin after that if we need to.
