Plants and algae use photosynthesis because there is by far more energy in sunlight than in cosmic rays or radioactive radiation; "by far" means many orders of magnitude. (You may have noticed that in most places most of the time there a dearth of alpha, beta and gamma rays...) Chemosynthesis, when available, is of course much much more efficient than photosynthesis; living beings which use chemosynthesis are usually called fungi or animals: they eat plants and algae. In your example, the algae will do the photosynthesis and the dinos will do the chemosynthesis.
Concrete numbers for algal dry biomass production vary widely, but as far as I can easily find they top out at about 0.6 g/L/day or 0.16 g/m²/day. (I would love to see better numbers.) For comparison, plain old boring wheat produces 5 to 7 tonnes/hectare/year, which translates to 1.4 to 1.9 g/m²/day, and maize (which is called corn in the U.S.A.) is about 1.5 times more productive. Algae have the advantage that they don't required arable land and that their cultivation is more amenable to automation; but they are far from being productivity demons.
You may have to do some serious genetic engineering to increase the productivity of the algae, because at present algae are simply not a serious competitor to cereals.
Containment is very highly species-specific and place-specific. Algae grow in water; if, for example, your production facility is in the middle of the Sahara I don't expect containment to be very difficult, provided you take care to avoid having dry spores exposed to high winds. After all, the world is not choking under a continuous biomass of algae... I'd say that inventing elaborate containment schemes is one of the fun parts of writing science-fiction; they don't have to be completely specified in engineering detail, unless needed by the action; protocols, UV scans, filters, chambers with negative pressure etc. come to mind.