Paint Shop Pro has handled PNG alpha transparency since at least version 6 or 7. When you initially load a PNG into it, it does not load the alpha channel. If you want the alpha then load it into a mask. Also, by default, PSP is configured to save PNGs without an alpha channel. Choose options when saving to PNG and then run the optomiser. From here you can switch on saving of transparency to the alpha channel. The settings in the optomiser should be retained for the next time you save a PNG.
It's not as nice as it could be, but it works.
Going back to the original topic. I don't like that it gets favicon.ico without being asked to, but I suppose it is the only way to display icons for files that cannot link to it, such as images. It is however, very bad form that they don't cache the 404. Worse still is the fact that they still look for it even when an alternative has been specified in the document that was requested. That is undeniably a bug because no one needs more than one icon.
Personally I'm inclined to say that it should look for the favicon.ico only for files that cannot contain links to it. For an HTML document that does not contain a link, it should not look. Web developers should not be allowed to be lazy or what you end up with is the horrible mess that the web was 3 or 4 years ago, and is still recovering from.