Cuz, in your photo with the warm water, I believe that you are reading the level shown at the top of the miniscus. With most of the higher end hydrometers I have used, the correct reading is the surface of the liquid (below the miniscus). All hydrometers will read differently between the surface level and the top of the miniscus.
In industrial settings, I use good quality Thermohydrometers (hydrometers with a thermometer inside to show the temperature correction factor) with a fairly narrow-band. These are needed as reporting the incorrect alcohol % on the label results in large fines.
In home settings, I have used both inexpensive hydrometers, and refractometers. At home, I don't really care about the exact ABV, I care more about an approximate value, and production of tasty beverages. Home hydrometers - like any piece of test equipment - will likely have some offset from the true value, but this offset will be constant - it won't change, so once you establish the amount of the offset, you can apply this to the reading to get a very close result.
The issue with all hydrometers is that the density of the liquid is partially dependent on temperature. All hydrometers have a temperature that their readings are based on. The correction factor is not the same at different gravities: A higher gravity will result in a greater error at a certain temperature versus a lower gravity. Thermohydrometers overcome this somewhat as their reading range is narrow, so the temperature correction is fairly accurate. For reading with home hydrometers, it's important to understand the temperature of the liquid being tested, and the correction factor needed.
A second issue is surface tension. I already mentioned the miniscus above, but the second impact here is that as CO2 bubbles evolve from the Must, they tend to stick to the sides of the hydrometer, effectively changing the reading. "Spinning" the hydrometer in the test jar helps with this, if the Must is not in rapid fermentation, but does not completely solve this.
Best practice is to take the sample, attemperate to within a few °C of the hydrometers calibration temperature, degass, then overfill a test cylinder and add the hydrometer and read at the surface level. Quite a bit of loss here for a small batch of wine!
At home, I have pretty much abandoned my hydrometers. I just use a wide-band refractometer that compensates for temperature. It was pretty inexpensive. I don't care about the exact ABV, I just want to know the starting Brix/Plato and when fermentation has stopped. I use the calcs at Brewers Friend for rough calculations between Original Brix, Current Brix / Specific Gravity / ABV. It's so easy, and the results are reasonably accurate.
TLDR. Your cheap hydrometer is fine. Get the sample to a close temp to the calibration temp of the hydrometer, spin when reading, and read at the surface of the liquid, not above the miniscus.
