You got it sort of half right -

a fatigue limit is the amount of stress that, if a material never sees stress above this limit*, it can theoretically never experience fatigue failure. NB that these stresses are always in the 'elastic deformation' range - minor deflections

Aluminum is known for not having a fatigue limit - any amount of stress, no matter how small, is likely to eventually lead to a fatigue failure.
It kinda sounds dire, but that is only a property of the bare material. Through design and engineering and construction, a part (in this case a frame) can be made to last billions of stress cycles. If you were to assume one pedal stroke = one stress cycle, and assume you move 2 meters per pedal stroke (700c wheels with a roughly one-to-one ratio, say 24-24), you get 2 billion meters of riding, or 2 million kms.

* 'if a material never sees stress above this limit' is a big 'if'. Designers and engineers will make assumptions about the type of loads a bike will experience, and try to design and construct a frame that can take these loads and no part of the frame will see stress above the fatigue limit, or in the case of aluminum or other materials without a FL at stresses so low that some high number of cycles (billions?) are expected. The problem is that the use the bike sees may or may not exceed the assumptions made during design. Also, fatigue is only one way a material can fail. Material can fail from a single extraordinary load, or it can corrode, or it can be constructed in such a way that the strength of the material is compromised. As a buddy of mine says, it's far more likely that your bike will die from 'misadventure' long before fatigue failure.


About the dent
First, I cannot see the pictures. But in general, if an aluminum frame is damaged but still ridable, it's almost always preferable to leave it as-is because every successive bend the metal sees weakens it significantly. The discussion of 'fatigue limits' is not relevant here because bending the metal to a point where it stays is 'plastic deformation' - beyond the elastic deformation range where fatigue limits apply. A single bend might reduce the strength by 25%(just guessing at numbers for the sake of discussion), but bending it back might reduce it another 40% or 50% or more (again, guessing), or it might crack as soon as you try the repair.
As long as the wheel still sits straight in the frame, leave it. If the wheel does not sit straight, then there is no reason not to try a repair as the bike is garbage if it can't be fixed anyway. But either way, understand that the strength of the frame is already compromised and treat it as such, and also know that any repair attempts will weaken it further.
This same logic applies to steel frames but they do generally have the ability to be straightened out a couple times before the strength is so compromised that they shouldn't be ridden.