Depends on the item and what you’re doing with it. If the product you are selling or giving away eliminates the need for somebody to buy the original item, then in most cases, you can’t sell it or give it away elsewhere. You can sell it on Envato if you have permission from the author and you’ve bought an extended licence.
If you just get a regular license, then you can give away or sell the end product to a client… but the client can’t then sell or give away the end product to other people. Although they can give it away if the Envato item is only part of a larger project, and it’s not possible to extract/use that Envato item from the end product.
So the answer to your four questions above are pretty much no for all of them… as they would essentially be stock items, whether sold or not. You could give away as a gift, but you’d need to buy one license per gift you give away.
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. 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, 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 sold via Envato.
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 without breaching your exclusivity.