If you have a form on your website - like form on the Contact Us page or an employment application page, you should be receiving, via email, whatever people submit (enter)... in a perfect world. Because there are email spammers out there, things don't quite always work this perfectly. Very often, these emails from your website get stuck in spam filters that you have running.
There are different kinds of spam filters. You could have a spam folder in your email program if you're using Outlook, Apple Mail or even GMail. Look for those emails there. You could also have a separate email service set up. With a spam filtering email service, they might have either a website to login to and find spam in a repository or something like that.
When your new website launches, it's important to make sure these emails get through. If not, you might have to set up the server on a white list or teach your spam filter that those kinds of emails are not spam.
No. With websites that Webstix sets up, we don't trust email because of problems we've mentioned. We always have a backup and it's going to be on your website. Check your website's Dashboard or Administration area (login there) and look for the "Forms" component or plugin. In that area, you should find a place called "Submissions" where a copy of everything sent it is kept as a backup. There, you can download/export it.
If you own a website with a shopping cart or e-commerce, you should never trust email. You should be logging into your website a few times a day to check and confirm orders. You'll also want to reconcile this information with your payment gateway software to make sure each transaction went through and was successful or that something wasn't missed.
If you're not receiving email that you think you should be, then find out if you have any spam/junk email filters in place.
Email can be set up a large variety of ways, so filtering might not be the issue but it's the best place to start since this is usually what is happening.