What Z artefact is this?

Good day for you all!

I'm currently in a possession of Aurora Z-605 3D Printer of Chinese origin. This is a Prusa i3 model with acrylic frame.
The print condition now is depicted in the attached photos.

- Lone cylindrical tower :
This single-walled print clearly resembles a combination of Z wobble and (some kind of) Z banding.

- Square tower :
This is also single-walled. The side to the left shows both Z wobble and Z banding, while the side on the right only has Z banding. The Z wobble only occurs on Y axis and leave it for now.

- Three cylinders :
These cylinders was varied by minimum layer time. The top cylinder has no minimum, the second has 5s and the bottommost has 10s. As the layer time increase, the cylinder wall become rougher and there also appears many gaps.

Now, for the printer settings, these are the things that I think has effect on this issue, although I'm not really sure myself.
The shipped firmware is of unknown origin, maybe actually Marlin, but don't know for sure. However, I already overwrote it with a fresh Marlin because the original firmware is greatly incapacitated, like the speed is capped slow, the acceleration is fixed, and many more. Consequently, I lost some fundamental settings, i.e., steps/mm and thermistor constant table. For XYZ, I don't have any problem for they can be easily calculated. The main problem lies in the extruder as I don't have any precise instrument like vernier caliper or thermocouple to measure the steps/mm for extruder and extruder temperature, respectively.
On the other hand, I know that Z banding usually occurs for imperial-sized threaded rod for Z axis. What I have is a TR8x8 (if I'm not wrong)-sized threaded rod that has 8mm pitch. Since the stepper has 200 steps/rev, it means that it advances by 0.04mm per full step (according to [prusaprinters.org]). At first, I though the banding is caused because I set the layer height at 0.25 which is not a multiple of 0.04mm. But changing to 0.24mm bears no difference.

I'm only a newbie in this kind of technology, so I think I need to rely on experts here.
Thank you.

The steps per mm for the extruder is generally an imprecise calculation, due in large part to the way it's measured (it's very difficult to mark and measure filament with any real degree of accuracy even with calipers). You end up fine-tuning the extrusion multiplier based on the results of the calibration process ([reprap.org]. Extrusion is affected by filament width as well, so this is something you'll end up playing with often. Regarding temperature, try the temperature calibration tower [www.thingiverse.com].

Acrylic frames lack strength compared to steel or aluminium frames, due to the inherent flexibility of the plastic. Push against the nozzle (please make sure it's cool first) and you will most likely see it move with little force. To counter, make sure your belts are tight, slow your print speed and drop your acceleration settings. There will be a reason the original speed settings were low and slow.

It's true that acrylic doesn't actually qualified for this job due its low strength. But till now I wonder, is the frame really that important? I mean, there are RepRap models that don't even have frame, e.g. [reprap.org] and [reprap.org]. I am quite sceptical about what kind of quality do these printer print.

Regarding layer height, since I have a 8mm pitch threaded rod with 0.04mm/step, must I have layer height that is a multiple of it? Can't the stepper microstep (mine is 1/16) so that it can achieve a finer resolution of 0.025mm/ustep and then I can set the layer hight more freely?

The point of the frame is to hold the rails in place, so that the axes move in the right direction. Those other printers don't have frames because they (hopefully) have some other way of holding the rails in place. I guess you could print (or otherwise fabricate) reinforcement pieces to attach to the acrylic to improve its rigidity.

There are many things wrong with the Prusa design and its offspring.

For the acryllic frames due to the way the x belt tensions and the right side plastic part the way it attaches to the horizontal rods you will see the rods go all the way through which causes the tension on the belt to pull the right side Z rod inwards. This in turn causes flex on the top of the frame squezing it causing it to curve. Look at your printer from the top sometime.

Ive done much to fix these issues on mine but in the end it really is loosing battle and im in the process of building a new printer and will pillage my prusa for its parts.

I want to print quality parts reliably, not forever fight with the darn printer.

Well that makes a lot of senses. But before I installed tensioners for both axes, the wobble went all way round, spiralling its way up in all direction. After I installed the belt tensioners, the wobble in the X axis diminished but it didn't go the same for Y. Doesn't it seems counter intuitive with the design defect you said? Btw, what do you hold the bearings for Z axis with? The X ends in my printer are kinda like this [reprap.org] . When I see the carriage going along the Z axis, the bearing holder, which is a near-complete cylinder-like, seems to stretch as it wobbles. Does this mean that this design is not so well, or that my lead screw is just too strong to bend the X end, or that my part is just getting weaker?

Despite the Z wobble, I have a banding problem that I can't think of any cause of. The banding only starts to happen after several layers and it occurs after every some layers. I have tried to change layer height and also changed the steps/mm thinking it were actually imperial lead but still not good.

The frame is going to flex more in the Y direction as the weight of the X carriage moves up, especially if your print speed is set high. Our printers use a frame stabiliser like this [www.thingiverse.com] on our aluminium-framed printers to keep everything stiff and square.

Try lowering the printing speed a bit to see if the problem reduces itself.