I've found that once the music files are transfered from iTunes music library to the device, you lose a greater ability to edit the properties or add artwork to the mp3s if you then try to then. It's hit or miss and I think it has to do with how the music with what software was used to encode the music files and what format they are in.
From these experiences, I've made it a habit of doing all the tag/properties edits and artwork adds in iTunes music library first, then move them over to the phone as the final copies.
Do all the editing on the computer, from my stand point (and most people's) this is where it makes logical sense to edit the media.
Then sync the media via playlists to the device.
Sometimes, although very rarely, sync acts weird and a reset of the device or re-sync is required to clear things up. When you say "speeding through songs" do you mean they are playing really fast, like 2x speed? There is a setting on the screen for 2x speed in the upper right hand corner.