How to calculate the voltage of the capacitor in this circuit?
Your \$\mathbf{I_L}\$ is correct, but your phase angle for \$\mathbf{U_L}\$ is wrong. An inductor's voltage leads the current by 90 degrees; you subtracted. The voltages are larger than the input because the circuit is reactive, but total power is conserved and you can check that \$\mathbf{U_q} = \mathbf{U_L} + \mathbf{U_C}\$ by cross-verifying \$\mathbf{U_C}=\mathbf{I_L}(\mathbf{Z_C} \parallel R)\$.

Edit: Here are the values I calculated with Python:

from math import pi, e    
w = 2 * pi * 636.62
R = 0.11e3
ZL =  1j * w * 8.5e-3
ZC = -1j / w / 10e-6
Z = ZL + (R * ZC) / (R + ZC)
U = 220 * e ** (1j * pi * -50 / 180)
I = U / Z
UL = I * ZL
UC = U - UL
IC = UC / ZC

def polar_str(x):
    from math import atan2
    angle = atan2(x.imag, x.real) / pi * 180
    return "({:7.3f}, {:8.3f})".format(abs(x), angle)

print('\n'.join(v + ' = ' + polar_str(eval(v)) for v in 
      [' R','ZL', 'ZC', ' Z', ' U', ' I', 'UL', 'UC', 'IC']))

output: (mag, phase)

 R = (110.000,    0.000)
ZL = ( 34.000,   90.000)
ZC = ( 25.000,  -90.000)
 Z = ( 11.567,   62.155)
 U = (220.000,  -50.000)
 I = ( 19.019, -112.155)
UL = (646.657,  -22.155)
UC = (463.659,  170.649)
IC = ( 18.546,  -99.351)