Well if you're unsure as to what your signal contains here is what I suggest:
If you're using newer scope then it should come equipped with an FFT option under the math menu. Have the scope compute the FFT of the signal you're interested in looking at. If for example you have s(t) = sin(2*pi*1000*t) + sin(2*pi*1000*t + 37 deg), you won't be able to make the distinction on the scope because the FFT is only a magnitude FFT, and not the phase FFT.
However, if you have for example s(t) = sin(2*pi*1000*t) + sin(2*pi*200*t + 37 deg), you will see 2 very large spikes at f = 1000 and f = 200. So that will tell you that your signal is composed of a sum of sines that have respective frequencies of 200 hz and 1000hz.
As for your second question. I believe you're thinking of ELI ICE. ELI - Voltage leads Current in inductive circuits. ICE - Current leads Voltage in capacitive circuits.
That is because if you are supplying v(t) = sin(w*t), and i = c*dv/dt (for capacitors) then i(t) = c*cos(w*t)/w. Which means current is leading. As if you'll recall cos(w*t) = sin(w*t + 90).
Conversely, if you're dealing with an inductive circuit v = L*di/dt, and the same math follows as above.
So, only in these special cases does current lag/lead by 90 degrees as you've stated below.