I'm confused with transparency on PSP (yes, yet again) images. I paste a picture of a dog on a swirl background with the "paste as transparent selection", and there's still that white block around it. If I overlap the custom brush again, it covers the dog picture. I tried uploading it with the GIF exporter, but that didn't work.

GIF transparency occurs when you set one colour (usually the background) to be "transparent," or ignored by the browser. So when you paste a transparent GIF, or just open it, into a graphics program, that coloured background will be there.

I unchecked the "transparency" box when starting a new image, but the white box was STILL there. How do I get rid of it?

You have to erase it manually. Like I said, the image isn't really transparent.