Let's go, Blackrune.
A lot of the finer points have already been covered and still stand, so I'll just address the two main mysteries.
The apartment: There is only one missing element here. How did Beowulf die in the locked room? The positioning of the body is key here, as well as one missing piece. Let's assume the bar he dropped is still in his pocket.
That bar, however, is not a silver bar. It is a powerful electromagnet. Unbeknownst to Beowulf, it is turned on (perhaps during a struggle with the culprit at some earlier point in time), sending a knife from the kitchen behind him hurdling towards him. The knife--lined up with the magnet in his pocket--sticks in his back and he flops forward, dead.
The wheel: The night before, Beowulf set up large sheets of clear plastic along the axes of the wheel. The effect here is to create a makeshift wind turbine. The next day, when it would be windy, the wheel would slowly--imperceptibly so--rotate. According to Beowulf's calculations, 45 minutes was enough time to shift a cabin over by at least one position. As described earlier, this created the opportunity for an accomplice--the culprit, Lykos--to stealthily undo the bolt and free Beowulf.
A second, more promising idea brought to you by DWaM:
Beowulf has a magnet on him, one that he can turn on and off at will. By turning it on, his cabin is attracted to the next metal spoke on t he wheel, causing the whole thing to turn ever so slowly, causing the desired shift.
If you prefer, he can load up the top of the next cabin over with a magnetic metal. The electromagnet would be attracted to it, as in the above case, causing the wheel to turn.
More red please.
The culprit is Lykos.
Ferris Wheel: tie a sturdy rope or tow line to the wheel, and then tie the other end to one of other attractions in the park that happens to spin or pull in such a direction that it would rotate the wheel. As stated above, Lykos, the accomplice and culprit, lets Beowulf out once the cabin is at ground level.
Apartment: As DWaM theorized, the blood trail was left beforehand. The window for entry remains the same. For the actual death, the culprit appeared at the window, startling Beowulf and causing him to fall onto his knife, killing him. This is after setting the chain, of course.
How about something a bit stronger.
The culprit is Lykos.
To create the disappearance at the ferris wheel, the culprit and Beowulf worked together. As any theme park employee would know, it is imperative that a ferris wheel is balanced. That is to say, people must be loaded such that the weight is equally distributed along the wheel.
Of course, Beowulf's request all but guaranteed that this would NOT be the case.
Once his cabin reaches the top, the accomplice enters the scene. He loads up the cabin just below the halfway point of the wheel--which is permitted by the previous red about venturing to the top of the wheel--with weight. It's likely they used a combination of their own body weight as well as another weight the accomplices had available to them: the bag of silver they'd stolen from the moon cult.
Using this approach, the wheel would rotate ever so slowly such that the two weighted cabins at 12 and 3 o'clock move clockwise. The accomplice can shift weight from the cabin they'd weighted into the cabin shifting to the new 3 o'clock position until Beowulf's cabin is within reach. Here, they unlock the bolt, freeing Beowulf.
If you want to be a stickler about how the top cabin was found locked, assume every cabin was locked beforehand, and only the cabin loaded up with silver is unlocked, then relocked as it that cabin "shifts".
Now for the apartment. We don't have much room to maneuver here. There really only seems to be one opportunity for the victim to enter here. Let's forget about the man caught on camera by Fenris: that's someone else, so Beowulf likely entered through an open window somewhere else in the building.
Our window of opportunity is the moment Wolfgang unlocks and opens his door. The blood trail in the hallway (the only part of it Wolfgang says is old/dry) was created earlier by Beowulf, from his leg wound. After Wolfgang opens his door, he sees blood going into his entryway, which is the first suggestion that the victim has already entered the flat before then. This is simply impossible, so I have to imagine Wolfgang is wrong here: he's in a bad state, so it's not hard to imagine that there were spots in his vision, making it look like the trail continued inwards.
So at this point, the victim rushes in, chains the door, and dies. But now we have another problem: death was instant, wasn't it? So who delivered the killing blow, and how did they escape?
This is just a trap. The narrative suggests that death was instant by appealing to the police's conclusion. But this simply cannot be true. They must be incorrect. If we operate under the assumption that the culprit killed the victim in the flat, we run into a sure contradiction when attempting to explain how the culprit disappeared from the chained room. Therefore, the killing blow MUST have been dealt outside the apartment. But the victim alone must then enter the flat, so the killing blow CANNOT mean instant death.
The victim, mortally wounded but still mobile, rushed inside in an attempt to save themselves. They chained the door, then perished next to it. This--the body resting against the door--explains why the gap was so small.
Why the incorrect assessment by the police? Fenris' fault. His feat of strength at the door buried the knife deeper into the wound and flung the already dead Beowulf into the position his body was found. Now, as far as the police would be concerned, the wound appears to have been an instant death.
The culprit is X.
Beowulf's cabin is locked by Wolfgang, and he leaves to operate the wheel. The cabin reaches the top. An accomplice uses one of the other attractions in the park to reach the top of the cabin and unlock it--perhaps some ride that just happens to involve a tower that ascends to the height of the top of the wheel. Beowulf then exits the cabin, locks it once more, then hops down from the top using the rest of the cabins as steps.
As for the murder, the victim is not Beowulf, but X, who looks identical to Beowulf. X used Beowulf's blood to create the blood trail leading up to Wolfgang's front door before Wolfgang's arrival. Of course, there's the issue of the blood trail continuing into the entry of Wolfgang's flat. Let's say the culprit drilled some holes in the floor of the apartment above and dripped the blood in from there.
While Wolfgang was distracted after unlocking his front door, X sneaks in, makes their way to the main room, then chains the door shut. He uses the rest of Beowulf's blood to finish the blood trail, then commits suicide.
Let's kick this off with a collaborative blue with @Bad-Player . No leprechauns, surprisingly:
The culprit is X.
X, who was working with Beowulf and Freki to steal the cult's silver, planned to frame Wolfgang for subsequent murder and theft. This is why the amusement park was chosen as the location where one of the culprits, Beowulf, would shake his pursuers.
To this end, X hid in the ferris wheel's control booth before Beowulf arrived. After making his request and riding up to the top, Wolfgang left the control panel. Here, X takes the short window where Wolfgang isn't observing the wheel to move it--after this movement, the box at the top of the wheel is no longer where Beowulf is hiding.
Next, the goons arrive, searching for Beowulf. The top cabin is searched, and as expected, no one is inside. Freki, who is in on the plot, is the one that mans the controls while Geri and Wolfgang search the other cabins. From this position, Freki fools Geri into believing they've searched every cabin. This could be accomplished with another movement while Geri and Wolfgang go downstairs, such that the "top" cabin is in fact searched twice.
Meanwhile, X, the person caught on camera entering Wolfgang's apartment, is lying in wait. Sometime earlier, he's made a copy of Wolfgang's apartment key, allowing him entry. Beowulf makes his escape from the cabin (either by breaking it open once everyone has left or with a sneaky unlock by Freki) and heads to the rendezvous point at Wolfgang's apartment. Beowulf enters via the open window of a different apartment (one of the two on the first floor, perhaps), allowing him to avoid detection by Fenris. He enters Wolfgang's apartment and gets stabbed, etc etc. In order to solidify the case against Wolfgang, he sets the chain and removes the door from its hinges, leaves, then replaces the door. If you prefer, a smaller "door" is cut into the chained door, evidence of which is destroyed when Fenris busts down the chained door. For good measure, he creates a fake blood trail leading to the front entrance of the building (this can be done before or after the murder), then hides upstairs in the apartment that Beowulf entered through.
If we want to be extra rigorous here and avoid running afoul of Knox's 1st, X can be either of the park's employees.
An attempt at the table impossibility:
This relies on the fact that Kelsie first saw every lock engaged, then watched from the lounge, meaning nobody could have been clearing the table before the ambush, while after the ambush there isn't enough time.
However, Dr. Mummies was hiding in the Kitchen or Dining room, not in his room. He set his own lock using the magnet trick to fool Kelsie. Thus, he could clear away the evidence undisturbed before the ambush. If necessary, he could do half the work before and half after.