Show us more dice being rolled!
Yes please! A part from just having that information easily visible, it would add to the fun seeing those attack rolls.
[Passive Perception]...these rolls should be made in the background and should only be shown on success.
Yes, if something is hidden you shouldn't be made aware of it, unless you succeed. A good DM would never do this. Maybe have this be tied to difficulty settings, or a toggle somewhere.
Shove: I also agree that Shove should be toned down a little, and I think it should be changed to an Action.