Various comments, the first as |i climb aboard one of my hobby horses.
Is the tool sharp? AND is it on the centre line?
If it is not it will, not cut properly. Too low and you have excess clearances. Too high, and the tool does not cut, it rubs because the cutting edge is above centreline, and cannot contact the work..
Tool overhang from the toolpost should not be any more than is necessary. The longer it is, the more flexible it is. And rigidity is important. A tool that is waving about in the breeze is unlikely to produce accurate work.
This is why industrial machines are massive, heavy and rigid.
A quick check for tool height, if you do not have a Centre Height Gauge (Easy to make) is that when the tool faces the work, (Cuts across to machine the end of the bar )and reaches the centre, there should be no "pip" evident.
If you want to see a picture of a centre height gauge, and instructions on how to make one, PM me, with an E mail address..
For what my advice is worth, start off with High Speed Steel tools, and learn how to grind them.
You may think that is worth investing in some books.
"The Amateur's lathe" by L H Sparey is old but a good starting point, tending to centre around the Myford ML7. But the principles are good, neverthe less. There are other books on Lathework by folk like Harold Hall, Neil Wyatt, Dave Fenner and so on. They may not all feature your particular lathe, but the basic principles are the same.
Neil Wyatt recently wrote a series of article on basic lathework, in Model Engineers Workshop. It featured the Sieg SC4 lathe, which is a big sister to your S2 (Neil is one of the many users of the SC2 lathe, and his book will feature it )
Carbide tips are not sharp. They were intended for heavy duty industrial machines to remove lots of metal, fast!
A good all purpose tool for turning and facing is a Tangential Tool (On another hobby horse! )
You can make your own. There have been at least two designs published in M E W, (for 1/8" toolbits )or you can buy the Diamond Tool from Eccentric Engineering. I have made several, ( for 1/8 and for 5/16" toolbits ), for myself and for others, including The WaterWorks Museum in Hereford.
What feed rate are you using? A fine feed would be about 0.004" (0.1 mm ) per rev of the chuck.
Too coarse a feed rate will produce a rough finish. You are effectively cutting a screw thread, of sorts!
You will always have backlash in the machine movements, otherwise nothing could move.
The machine is new, so backlash should not be excessive. If it ain't broke; don't fix it!, You might make things worse!
Whereabouts are you located?
Hope all this rambling is of some help
Howard