By which software/website this animated video was created?
As for video editing, this is pretty straightforward. The frame and the flowers are simply an image that has an alpha channel applied to it to make the contents of the frame opaque. The images in the frame are static (as in not animated) images with crossfade transition (as well as a static background image). You can do this with pretty much any video editing software.

As for the illustrations, I'm pretty sure they were created with Adobe Illustrator (or any other vector graphics software). While the editing for this video is super easy and can be done by anyone, I would recommend you hire a professional illustrator if you want to create something similar but don't have experience in that area (and don't want to have to rely on stock images/illustrations).