Azaleas do much better than rhododendrons in the south. The shady areas you have should be fine for azaleas and hydrangeas as long as the shade is bright (not too dense for too much of the day). The rhododendrons may work but would be more risky and picky about growing conditions. The best planting time is in fall or late winter.
The following two websites will give you much more information on growing these plants than I can fit in this brief reply:
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