As a side note, the web app is hidden -- they want you to download the desktop app, from which you can't block ads. The thing is, the desktop app performs even worse than the web app
However, as far as user experience goes, I don't share your experiences at all – the web player is almost unbelievably bad, with frequently malfunctioning (disabled) player keys, volume slider jumping all over the place and common problems when resuming playback after a while. (Also, the desktop application has more features, including the ability to select multiple tracks to perform an operation on, and naturally the support for media keys.)
As for your first question, I think when it encounters what should be an audio ad in the queue, it attempts to play it, due to the host file, the ad request gets blocked/sent to a black hole and nothing is returned, so the application presumably assumes that everything was fine and continues on.