1. Login always fails
In some edge cases the mobile API of Last.fm doesn't handle login properly. If you do encounter this rare problem, try changing you password on Last.fm then you should be able to log in. Sorry for the inconvinience.
2. Why my repeated plays are timestamped at one single time point?
Due to the limitation of iOS system, iOS only keeps the last time point of a song you've played, so currently the repeated plays are timestamped based on your last played date. Let's hope a better solution would come to iOS eventually.