LTspice – Function for Multiplying Two Voltage Waveforms

Ground is a notional "0V" point : all voltages are referenced to it. In principle it could be applied to any node in such a simple circuit; however the usual convention is to choose the -ve terminal of the voltage source (or any point directly connected to it, i.e. on the same net). Any other choice runs the risk of confusing people!

If you have a fixed frequency then you can use definite integration over one cycle to eliminate the DC. It will take one cycle for the circuit to respond, true, but you can skip that (unless you;re interested in transients, too). To avoid repeating, here's my answer giving the solution to this. I'd advise using the G+C variant, rather than the behavioural source, as the delay given from the tline is much more reliable, but the choice is yours.

If your frequency varies, then you can simply use a lowpass filter of your choice (in LTspice, avoid Laplace in .TRAN analysis). For a simple example, a 4th order Butterworth:

...or a 4th order Bessel, for almost linear phase, normalized to -3dB (see the 2.114 in .param f=1/2.114 is the frequency scaling factor):

If you DC point also varies with frequency, you're better off using the non-normalized Bessel, to have a better group delay in the passband, and to use a tline to delay your reference signal to match the Bessel delay, something like this:

Note that the way the input is delayed is just an exemplification, the way I did it, since I don't know what you have in your schematic. At the very worse, you could add a G source followed by the tline and the terminating resistor as seen in the example above.