The inverted time physics in Tenet is coherent enough to support the plot but if you think about it long enough it falls apart in many places. There are plenty of funny things that happen that have a more or less logical explanation, an extrapolation of what time reversal would look like if it were possible. But many things end up as contradictions. When you see the movie it is OK because you don't expect to understand everything.
The movie presents the wall with bullets and other artifacts as remains of a future war. So you imagine a future war with part of the world reversed, someone shoots at a wall, some machines break and fall apart, and all this ends up burried. Since it happened in inverse time, the remains of these events move backwards in time and end up burried in the present time, where they are dug out.
But that doesn't add up. A bullet has a single timeline and is shot only once. It doesn't get shot and "unshot" by somewhere else. At least that is not how the plot works: "What happened, happened." Since we see the protagonist shooting the bullet (even though in reverse), that is when it happened. The bullets in the wall were shot by the protagonist, and never and nowhere else in the future or the past.
Another interesting question is: where did the bullets come from? Since they come from the future, to see where they come from, you have to follow their timeline back in inversed time, which is forwards in normal time. You just need to see where they go. And they go into a storeroom. If the bullets come from the future, and in the future they are in the cupboards in a storeroom, that that is how they came to the present time. Someone in the future must have reversed himself and placed the bullets and other mechanincal parts in these cupboards. Not quite the story that the movie suggests.
- When should the bullets have appeared on the wall from the forwards perspective?
From an inversed perspective the wall disintegrates slowly, the bullets rust, and end up as dust. So, from the forward perspective, patches of rust spontaneously "unrust" into bullets, the wall resolidifies around it until it gets dug out.
Possibly the wall was reversed in the past. If so, it appeared simultaneously in its forwards and inverted form on both sides of a turnstile.
- Were they shot when the gun was still uninverted?
Not, they were shot by the protagonist. It is not what the movie suggests, but it is the only way it could happen in a coherent way.
- What happens if you close the drawer with the bullet casings? Does the gun just not unshoot?
The philosophy of the movie is "What happened, happened". So the casings must be where and when they were needed. We don't know what would happen if someone prevents things to happen because in the movie it is never done.
- Was the protagonist pulling or releasing the trigger?
That is one place where the details become messy. In theory, in an inversed shot it is not the finger that pulls the trigger, but the trigger that pushes the finger back. But how that works with a gun that wasn't inverted in the first place isn't quite clear.
In the movie, the instructions Barbara gives are "aim and pull the trigger".
- Is there a difference between a forwards person shooting an inverted gun and an inverted person shooting an inverted gun?
The inverted person firing an inverted gun won't notice anything unusual.
For a forward person firing an inverse gun the gun behaves in a must unusual way, as you can see when the Protagonist shoots the inverse gun.
From the point of view of the inverted gun it is like being a forward gun operated by an inverse person. An inverse person is just pressing and releasing the trigger for a short time whether it is seen forwards or backwards.
It is not clear how the shooting action is being coordinated between a forward person and an inverse gun. At some time an inverse bullet jumps out of the wall just as the Protagonist decided to press the trigger. These two events join into the firing of the gun.
- How was the protagonist able to undrop objects?
I would say the idea is that reversing entropy changes the direction of causality. While normally the past determines what the future will be, inverse-entropy objects impose to the past to be what it needs to be for the future to happen. From the inverse perspective the hand opens and the bullet falls, so from the forward perspective when you see the bullet jump up you just see the consequence of an action that didn't happen yet, but is bound to happen because you already have seen the consequences. It is unclear how it affects the protagonist's free will to prevent him to not close his hand after all. He can't act otherwise because "What happened, happened."