Professional-only Features

Some features that are only available in the professional edition are pretty simple to implement, such as dhtmlX Tree’s openOnItemAdded method. I believe the GPL permits any modification, but I am not entirely sure. I know that I would have to release all my project’s code under the GPL if I use that license. Is there anything preventing me, in the license, from implementing these features?

No, you can modify the source code of dhtmlxTree Standard the way you need. Like you said, you’ll just need to distribute it under GNU GPL.