Makikisawsaw lang po.
1.) With regards to cartridge downforce adjustment, It says that the armtube should balance out does this mean that the arm should somehow float over the record.
When starting, get the tonearm balanced (arm should float) and set the vertical tracking force to zero. Then, adjust the vertical tracking force through the tonearm's counterweight at a figure recommended for your cartridge. If you're using the ULM Ortofon (OM or Concorde models), it should be about 1 gram. If it's the bigger Ortofons, set VTF from 1.5 to 2 grams.
2.) The tonearm came with a prefitted Ortofon cartridge, there is a section in the instruction manual about adjusting the azimut (what does this mean?) do I still need to do this even if the cartridge is prefitted?
If your record deck is pre-fitted with a cartridge, it should have the correct azimuth (diamond stylus sits perpendicular to the record groove ensuring optimum contact for left and right grooves that correspond to recorded left and right channels.) If you were provided a gauge, use it to confirm that the adjustment is okay. Ocular inspection and adjustment, by using a mirror and small screwdriver, could help you if you don't have a gauge.
3.) One of the parts included with the turntable is an anti-skating weight is this an essential part?
Yes, very much. The anti-skating adjustment would prevent your cartridge from sliding in or resisting correct tracking of record groove. The anti-skating force is generally within the range of the vertical tracking force. Thus, if you set at 1 gram VTF, set the anti-skating force also at 1.
In many cases, adjustments in VTF and anti-skating are "oido" or depending on what you hear. In my experience, the higher recommended VTF gives the best sonic results. But it also increases wear of the record grooves. Btw, very low VTF setting aimed at saving the record is also harmful since your stylus would cut into the vinyl resulting in tonearm/cartridge jumps. The same is true for wrong anti-skating force. Inaccurate setting would also increase diamond stylus wear.
Analog requires a lot patience and hefty investments nowadays. Still, congratulations and hoping you'll enjoy your new toy.