Find the inductance using function generator, oscilloscope, capacitors, resistors, multimeter, voltage generator
1 you do not need a current probe. Put an ohmic resistor in series with inductor and measure the voltage over the resistor

2 capacitor and inductor do not change an input sine wave, only the amplitude and phase

3 not much to say

4 where are you putting your oscilloscope probe? Put a series resistor with your inductor and try to read over the inductor. If the sine keeps the same, maybe your inductor has a low inductance. Try to lower the frequency of the sine generator