Can I get the dragon balls more than once? If so how?

No you can't.

At this moment you can only get the Tier 1 balls wich you get from quests. The balls you can summon more than once are the tier 2 balls. Those you need to get a chip for your scouter to see wich mobs could drop em durin the ball hunting events. Obviously the event isnt available yet!.
I hope i helped you clearing teh doubt :). Have a nice day ;D

Are they only available during ''DBall hunting events'' or it can happen anytime to find a DBall mob around your area ?

Only during the event.