Without backlash it would be impossible to move one part relative to another, so must allow for the backlash.
So if you put on a cut of 0.02 mm but overshoot to 0.025, all is not lost.
Withdraw the tool by 1.00 mm. Advance to Zero. Having taken out backlash, you wind in a further 0.02 to where you want to be.
Without taking out the backlash, accurate, or consistent results are impossible.
As a newbie you will learn a lot from books on model engineering.
"The Amateur's Lathe" by L H Sparey..
Neil Wyatt and Dave Fenner have each written books on the mini lathe.
Ian Bradley's "The Amateur's Workshop" covers general techniques
A set of Zeus charts is useful, for many things, plus Tubal Cain's "Model Engineers Handbook " a frequently consulted reference book, on many things.
The mini lathe is a hobby machine designed and built to balance cost versus accuracy and durability.
It lacks the power, accuracy or features of an Industrial Tool Room lathe, or costs as much!
Similar, if not identical machines are available from suppliers specific to the model engineering trade, such as Arc EuroTrade, Chester, Warco, Amadeal, or SPG – to name a few. These are more likely to be able give advice, as well as many on here, than Machine Mart, where knowledge may well vary from branch to branch.
The above suppliers may provide advice and help even if they did not supply the machine.
Where are you located?
Find a model engineering club local to you, and join. Again, advice, help and, Covid permitting, even face to face demonstration, may be possible.
Within its limitations, the mini lathe is capable of good work. Careful adjustment and skill can produce outstanding results.
Do not expect a 3 jaw chuck to hold anything without some run out (eccentricity ) There are very few 3 jaw chucks without run out, Many in good condition ( even brand new  
may yet show run out of the order of 0.10 mm A worn or damaged chuck may be even worse, I know of one very old chuck showing nearly 1 mm run out.
Diameters that will,be concentric to each other, as long as they are cut without disturbing anything between cuts.
The taper that you found could be from a variety of things.
1 ) How far was the material into the chuck jaws? For what you are checking, it needs to be gripped by the full length of the jaws. This assumes that the jaws are clean, both where they grip the workpiece, and where they touch the scroll inside the chuck.
2 ) Is the chuck clamped accurately to the flange on the mandrel? The flange and the register on the back of the chuck must be clean, and free from any burrs. If the chuck is misaligned, you will have problems.
3 ) Are the bearings in the Headstock worn or lost their preload? If YES to either of these questions, as a newbie, this is not work that you should undertake without finding out the correct way to check and then rectify the problem.
For this you really need expert attention.
4 ) Were you trying to reduce from 25 to 20 mm in one cut? 2.5 mm in one cut is heavy work. (My handbook says that 0.010" – 0.0025 mm is a roughing cut, although many take far deeper cuts without damage) Lacking the handbook, get one.
For your checks, a cut of 0.05 mm might be more suitable, since it will cause smaller deflections in the machine. Also, your feed rate needs to be slow. Forcing the tool will cause deflections.
Using changewheels and Leadscrew for the feed, a 20:80/20:80 train should produce a feed rate of 0.0937 mm per rev.
5 ) Is the cutting tool sharp? Don't expect good results from blunt / chipped tools.
6 ) Is the tool mounted with the cutting edge is on the centre line of the Headstock?
Quick check; face across the end of a short piece held firmly in the chuck. Off centre the tool will leave a pip near the centre of the work.
A tool above centre will rub rather than cutting properly. A tool, below centre will have the wrong effective angles to cut properly.
Both will need extra pressure to cut, if at all..
7 ) The gibs on the Cross Slide may be slack, allowing movement. Until this is minimised, consistent results are unlikely. The saddle should be located by the Vee bedway, but if there is vertical movement accuracy will be impaired, so that is another adjustment to optimise.
With a second hand machine, you cannot be certain what use / abuse / misadjustment has taken place.
(I bought a secondhand lawnmower. Worked far better once the blade had been fitted the right way up! )
Hence the machine needs to checked over, and excess play removed.
8 ) If you were turning between centres, one of the centres could be "out" and need cleaning up, or the Tailstock could be misaligned.
Easy to rectify, but needs measuring equipment to do as accurately as possible,.
9 
Disaster scenario, AFTER you have checked all the foregoing, it is possible, but unlikely that the Headstock is out of line with the bed. Again extra knowledge and measuring equipment is needed to confirm and correct it.
Sorry to ramble on on such length, trying to cover as many options as possible.
Howard