Yes that where I grow more for the town. The only problem is villagers will plant flowers in the empty spots. The more time you spend on the beach the more the villagers show up. One evening I was trying to catch fish for the museum and the villagers started to show up. By the end of the night I removed 2 pockets full of flowers.
Yes they can.To get them growing fast I recommend fertilizer,watering every day and no time traveling.I started with just two purple pansies.This is actually cultivating rather than breeding but either one can be done on the beach.