These are set by the website, the site designer has to make a .ico file and upload it to the webspace.
There probably isn't an easy way to change them yourself.
To save space I edit and abbreviate or remove the text if they are distinctive enough.
You can also make a folder and indeed subfolder by category, and drag them to it.
From time to time some icons will revert to a sort of blank placeholder then pop back to normal after visiting the site again.