WebP is the format most modern sites serve, so it is what you get when you save an image from the web. It is efficient, but plenty of desktop software, older design tools and some content management systems still refuse to open it. Converting to PNG gives you a lossless file that opens essentially anywhere, with transparency intact.
Yes. Both WebP and PNG support an alpha channel, so transparent regions come through unchanged. This is the main reason to choose PNG over JPG as your output here.
No. PNG reproduces exactly the pixels the WebP decodes to. If the original WebP used lossy compression, those artefacts are already baked in and will be preserved faithfully, but nothing new is lost.
Compatibility, not quality. WebP is excellent for serving images on the web. PNG is what you want when a specific application, printer, or older operating system cannot read WebP.
No. This converter reads the first frame only, because PNG is a single-frame format. For animation you would need APNG or GIF, which this tool does not produce.