I created a private pool recently intending to gather my favorite pics to download them more conveniently, but the fact is that when I'm trying to download, there's always a 404 error. Considering that pics downloaded from a pool before are in a zip form, I'm wondering if there's any missing procedure before a download.

There is no such thing as "private pool". howto:pools

Creating pool just to batch download images will just get you banned.

As for why the zip didn't work, I don't know.