If you think about it, this would be a good thing for shops especially so people can actually 'know' what they are paying for ... or if someone is trolling and the chest isn't full or whatever. Coding wise - this is very easy - with exceptions ... with a [view] sign nearby - a player would not be able to view the chest by opening the chest itself because the player who owns the chest wouldn't be able to move anything - because the first thing for a view sign to be possible is when the chest is being interacted with for a 'view' sign reason ... would need to have block interaction and being able to move items in and out and to other slots in the inventory. By opening it by right clicking the sign however, you'd be accessing it from another method and you can just have a player chest gui appear for the individual player and have the item's within the slots of the gui be copied from the chest near the view sign - but not allow for player interaction. Edit: I thought about it ... it would be possible chest wise - just you'd need to have it be like If the player's container permission is true then allow for block interaction within an inventory within the residence to that player. If a player's container permission is false and a sign that contains the wording view is located near an inventory, then block interaction within an inventory is set to false within the residence for that player.
I don't think it would need to be limited to just one. Look at how the new mail system works, I think it's 6 slots. It would really just depend on who designs the feature.
The inventory that you see when you open 'any' container object is actually your own player inventory. The mail feature is a chest ui. Which is a separate slot system from your player inventory slot system.