If you are wielding a shield, is that arm/hand available to be used to hold another item or object? Or is that arm/hand completely occupied by the Shield?
RAW, Your hand is occupied.
The description of a Shield in the PHB states...
Shields. A shield is made from wood or metal and is carried in one hand. Wielding a shield increases your Armor Class by 2. You can benefit from only one shield at a time.
Emphasis Mine from PHB p144
Thus, the PHB seems to be referring to shields that are 'held' with the hand, not simply 'strapped' to the arm.
In the medieval era, this was the norm. You'd either have a handle you gripped, a handle + a strap, or two straps (but you'd hold one of them in your fist). If you just strap a shield to your arm and don't have it mechanically affixed to your armor or something...the first time something hits it, it's just going to spin, hit you in the face or legs, and then be useless...because there's nothing holding it in place.
So, the back of your shield probably looks like this
or like this
Not by RAW.
A shield is made from wood or metal and is carried in one hand.
Based on this wording, a shield is carried in your hand, which means that you cannot carry another object in your hand.
As a DM making a ruling, I would probably allow some leeway, but the wording is pretty clear.
Yes, of course.
Clearly a character can't use both items at the same time, but holding a small object in the shield hand is easy. Just ask this authentic Viking...
I know the rules don't explicitly state you can, but I don't think that's how 5e was intended to be read or played.
But I'm likely wrong.