Ernie_C might correct this as I could be wrong, it appears to me that the start over feature is a shortcut to catchup.
Regarding picture quality if you are watching iPlayer it should be in HD, if you have never set this go into the app, settings, settings & help, video quality, and select best quality.
Sorry Ernie I didn't see your answer but it still confuses me as to what is available and what isn't, I will post an example.