until when people can post their stories and still get a prize?

It depends of how many people take part. When a minimum of stories has been submitted, you may submit another post as reminder and set the time limit.

Is upvoting the best criteria ? Steemit users who have more "power" can influence too much?

Personally I do not care much about users with higher Steem Power influence if all of them are related to Gridcoin.