There’s a library specific option to store track progress (or not).
Make sure you disable that if you don’t want tracks to continue where you left them the last time.
In Plex Web: ⋮ > Manage Library > Edit... → Advanced > Store track progress
As for your second question:
Your server home screen customization should already apply (e.g. published collections should also show on the Plexamp home screen. Beyond that:
