is it possible to create forms that save to the DB & a new screen in admin to see the submissions?
Is there a user created forms module (like gravity forms) for Craft?
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For now, you can create forms and create entries through the plugin Guest Entries.
In Guest Entries, entries are disabled by default.
Sprout also has a plugin for creating forms, that is currently in beta.
Is there anything specific you are looking for, or would you just like to be able to receive submissions from site users?
If you give some more information, we might be able to give you some better advice, but the Forms Market is still pretty thin.
Would you say those forms are always the same in the context of a site? You don't need a form builder for that (?), unless they are always changing and adding things. Even then, you can make a rudimentary form builder by using Matrix.
The notifications part has to be be added by a custom plugin. You can hook into the onSaveEntry hook, for example.
I built a notification plugin that does that, which sends of an e-mail and a sms to the site owner when entries are added through Guest Entries.
Subscribing to MailChimp is also fairly easy. You can have a look at the MailChimp Subscribe plugin as an example.