My friend suffering from right kidney hydronephrosis-ii with dilated ureter, 10mm calculus almond shape in upper ureter, can it expel without surgery?

No, not likely. Stones greater than 5-6mm in the upper ureter are unlikely to pass without some sort of surgical intervention, be it extracorporeal shock wave lithotripsy or laser lithotripsy with ureteroscopy +/- stent placement. A urologist can recommend the proper treatment to get your friend stone free and feeling better.
Possible, unlikely. Studies have shown that most stones under 4 mm and lodged in the ureter will pass. Those over 8 mm are not likely to pass and surgery is recommended. Those between 4 and 8 mm may pass and a 3 week wait with medical therapy is indicated.
Nephrolithiasis. Although it is possible for the body to pass a larger calculus, it becomes less likely with one greater than 0.5cm. Leaving the stone puts that kidney at risk for obstructive uropathy as well as debilitating pain and pyelonephritis (among other complications). I recommend following your urologist's guidance: typically flowmax & analgesics is non operative management but this may need intervention.