to win or to get candies?

Hmm, "win" has a connotation of earning it, not just getting it. You probably wouldn't say that kids win candies when they trick or treat. They would win candies at a fair if they pop a certain number of balloons... for example.

Can I say the children gain some candy?
Can I say the children gain some candy.

Re: to win or to get candies?
Children go shouting "trick or treat" from door to door during Halloween hoping to be given candy (or sweets in England).

I would choose the second choice you offer, with a slight change... I would use the singular for candy. I agree with Soz about the connotation of "win".

Children go shouting "trick or treat" from door to door during Halloween cecause they want to get candy.

Receive candies?

Yes, so to summarize, in my own words..

win = to win a contest, and if a prize is awarded from this contest, you could say that you won the prize which means simply that you acquired it by winning the contest

get = acquire, by any means

gain = to acquire something that makes one better. recieving candy doesn't really make one better which makes it an odd use in my opinion.

given = to get by voluntary donation

recieve = same as given, except it is not necessary voluntary