I have only seen it done to increase voltage. On some power supply front-ends (AC/DC conversion) with a voltage doubler the capacitors are in parallel at low voltage
and in series at high voltage. This works out well since for a constant power out
the current is double at the lower voltage.
As you mention balancing resistors are required.
Your gap is too wide. Make it very, very very narrow. And rolled into a cylinder. Like a real capacitor.
Yes, +q could be less than -q, but only if the attraction/repulsion effects of electrons in the connecting wires were nearly as large as the attraction/repulsion down between the capacitor plates. (In that case the plates wouldn't be a near-perfect electrical shield for the fields produced by the wires.) But with real-world capacitors, this doesn't happen, and instead the field between the plate is totally enormous compared to the tiny fields produced by electrons in the wires. If +q only differs from -q by a millionth of a percent, we ignore it. See Engineer's capacitor vs. Physicist's capacitor, a split metal ball, versus two separate balls.
For capacitors used in circuitry, if we dump some charge on one capacitor terminal, exactly half of it will seemingly migrate to the other terminal. Weird. But "physicist-style capacitors" with small, wide-spaced plates are different, and an extra electron on the wire will make +q not equal to -q.
In detail: if the capacitance across the plates is 10,000pF, and the capacitance to Earth of each wire and plate is 0.01 pF, then the opposite plate's charges will ignore any small +q and/or -q on the connecting wires. The attraction/repulsion of electrons in the wires doesn't significantly alter the enormous +q and -q on the inner side of the capacitor plates.
Engineers use real-world components: wide capacitor plates with very narrow gaps; gaps the thickness of insulating film. But if you were a physicist, your capacitors might be metal spheres with large gaps between, or metal disks where the space between the plates was large when compared to their diameter. (Or you'd draw a capacitor symbol where the gap between plates was enormous and easy to see.) In this case the attraction/repulsion of electrons on the connecting wires would have an effect on the balance of +q -q between capacitor plates.
PS
Another weird concept: make a solid stack of thousands of disc capacitors: foil disk, dielectric disk, foil disk, etc. Use half-inch wide disks, and stack them up into a narrow foot-long rod. Now connect one end to 1,000 volts. The same kilovolt will appear on the other end! The rod is acting like a conductor. Yet its DC resistance is just about infinite. Series capacitors! Each little capacitor induces charge on the next and the next, all the way to the end.
Best Answer
Capacitors in series are like resistors in parallel, to get the total capacitance add the reciprocals, then take the reciprocal of the result.
For example, if we have 20pF, 10pF, and 5pF caps, the total capacitance would be:
1 / ((1 / 20pF) + (1 / 10pF) + (1 / 5pF)) = 2.857pF
For two capacitors you can use the (C1 * C2) / (C1 + C2) but this won't work for 3 or more.
Note that putting multiple caps in series probably won;t work very well at such a low value (there will be extra unwanted inductance which will lower the resonant frequency)
2.2pF is actually a very common value, for example Farnell has 46 options under RF caps and 94 options under ceramic caps. I advise picking one of these.