EDIT: I just checked the code: When you opted to show local lyrics, it will also use the font size used for local lyrics. Are your devices maybe synced via iCloud? In that case, changing the font size on the bigger iPad will also change it on the smaller. You can adjust that with Lyrics > Device Font Size Modifier which is a setting that is only stored locally.
Regarding the auto hiding of the song list: I guess this is another bug. If the user enabled the option to auto hide the song list during playback on the client, it should also respect that setting when connected to a remote host. I will also fix that in the next update.