The hire rewards are connected to a successful hire, while the rewards in the reward shop can be redeemed by using the coins, which can be gathered both with successful hires (if the reward plan includes coins) and with activities (one point = one coin). Read more about the Reward shop and coins in this article.
There are two opportunities to decline a reward for a successful hire, read more about them here.
No, coins cannot be added or deleted by Admins, but just accumulated by the Talent Scout with the different activities and gained as a reward for a successful hire. Please take a look at how to earn coins here.