1) not sure of how ml works, but spice simulators are smart and regulate the time step depending on how confident they are of the solution they found. With (co)sinusoids they usually are very confident and you can see 4 or 5 points per period, connected by straight lines (linear interpolation). Solution: force Matlab to use your timestep, set it to 1/10 of the period or less.
2) either post process the data, subtracting the average calculated on a single whole period or on a large (100ish) number of periods, or AC couple your voltage probes. Since you are doing circuit simulation I would go with AC coupling. Put a big (some Fs) cap between the voltage probe and the node you wanna probe, and a big resistor (1G) to ground, on the voltage probe side.
3) This is not so easy. Try manually tuning the 1.4 M resistor and see if you can obtain reliable operation. If you want an automated circuit to do this for you, it is an entirely different question, search for Automatic Gain Control.