I was wondering if it was possible to use a video, purchased on envato (videohive), as a background to create another video? And then, put it up for sale on other stock agencies?
In one word: NO
But you can buy an extende license and IF the user allows you in writted form to use the video in other project then you can do it.
Read here: https://videohive.net/licenses/video?license=video_media_single
Can I purchase an item to use as a smaller component within a larger project that I plan to sell as stock or a template? For example, could I purchase a button graphic for a theme I plan to sell?
Use of items in larger stock projects is not allowed as the default position under the licenses, but there are exceptions.
Exception 1: When you purchase an Extended License and get written permission from the original author to use in your stock item sold via Envato and/or outside of Envato (as applicable). Keep a copy of the email giving you permission.
Example: A CodeCanyon author has a slider and gives permission by email to a ThemeForest author to use the slider, under the Extended License, in a theme.
Exception 2: When an author gives a blanket permission (in the item description) for the item to be used in other stock items sold via Envato and/or outside of Envato (as applicable), with the purchase of an Extended License. Keep a record of this permission if you use an item in this way (e.g. save a screenshot).
Example: A CodeCanyon author has a slider and states in the item description that any buyer is permitted under the Extended License to use this item in a larger stock item that will be sold on Envato Market.
Exception 3: When the smaller component is licensed as 100% GPL, you may use it within a larger stock item without needing special permission from the author.
Can I allow another Envato author to use my item within their stock item?
Yes, with the permission of the original author an item can be used inside a larger stock item or template.
If your items are exclusive, you can’t sell or redistribute them elsewhere or on other sites outside of Envato. But you can give another Envato author permission to use your item in another, larger stock item (of a different scope and nature to your item) that is then sold via Envato, or even outside of Envato, without breaching your exclusivity.
However, it’s important to remember that if the author of that other, larger stock item is exclusive, they must comply with their own exclusivity requirements when making the larger item available.
For clarity, being sold via Envato includes any/all of the platforms in the Envato ecosystem (e.g. Envato Market, Envato Elements, Envato Hosted etc.)