User Form in Gray

I looked at your form and the issue is how fields are styled. There are several stylesheets included with the plugin. You can choose a different stylesheet or set up a custom stylesheet. In your case, I would suggest creating a custom stylesheet to best incorporate the form styling into your theme.

http://rocketgeek.com/plugins/wp-members/users-guide/customizing-forms/

doesn’t show the entered fields once submitted from the back end side for approval.

You have a lot of things going on in this set up. So unfortunately any direction I give you could end up muddled since we may not be talking apples-to-oranges.

The plugin sets up some default fields and you can also create custom fields (and/or remove any of the defaults that are not WP native). If you are using another plugin in addition to WP-Members, those fields may not necessarily match up. Just because a field says “Address” for the label doesn’t mean that one plugin’s address is the same as another. In the case of WP-Members, you can set whatever meta key you need to for a field so you can match it up with any other plugin that uses custom fields that are stored as single entries. So if another plugin has an address field with the meta key “address” then you need a field in WP-Members to match that.

Also, my new user notification emails don’t seem to be coming through.

The simplest thing I could recommend is to just set up SMTP for sending emails. 99.99% of the time if there is an issue with emails going out it is related to some restriction either on the sending or receiving end for what qualifies as an allowed email by your host or the receiving server. That could be “from” headers, reverse domain lookup, or a number of other things. Sending via an SMTP server will eliminate those issues.

There is an article here about possible issues and also a discussion of SMTP:

http://www.butlerblog.com/2013/09/24/troubleshooting-the-wp_mail-function/