By parallel, I assume the plates will be physically parallel with each other, not electronically parallel (divides up the amperage). Watch out what kind of electrolyte you use with that plexiglass box, I know that KOH and NaOH will each react to some materials (one reacts with plexiglass, I believe it's KOH).
12V per cell (120V total) is a bit high, I think. The idea is to have low volatge (close to 1.2V), and high amperage. If you can find a way to tone down the voltage per cell (1.2 is about ideal, 1.2 being better, and 2.4 is fine), and keep the amperage that high, by all means, do so. High (relatively) volatge and amperage combined do boil the water (remember, high resistance equals high temperatures, R=I/V, resistance= current/voltage. Ohm's law. Keeping the volatage low (ideally at a minimum to perform electrolysis) keeps the resistance low, and therefore the temperature. Less boiling, and a closer to "true" gas output. Of course, if you want some vapour output (kept at a burnable concentration), you can fiddle with the voltage until you get a good ratio. Sorry I can't help you more with that, I don't have mush experience with it.
To put it simply, yes, your fears are valid, and the gas does have a chance of igniting once it reaches a certain temperature and amount of boiling. Best to keep that under control. And, always make sure you have a working bubbler, and keep the gas amount in the electrolyser at a minimum, less bang if it does ignite.
With most designs, keeping the space between the cell stack and the box small is a good idea, it helps prevent leakage (current skipping over cells, making some inactive and useless).
Remember to take pics and jot down measurements and values. Personally, I'd like to see how well such a large number of cells performs, when it's done by another less experienced person (like myself, and if you're not (which I can't know), correct me). Experiment with different voltages and amperage settings and setups, find what's most efficient. Good luck.
