Offering in-game store discounts and offers

I'm working on an infinite runner style game and would like to implement bonus features such as:

1. The ability to offer discounts on powerups/outfits etc. from the store during certain promotion periods. For example : X costs 500 coins instead of 2000 for the next 2 days. These are not in-app purchases with real money, but purchases with in-game currency.

2. Daily offers such as "Collect 500 coins today by doing X"

So I'm wondering how I should implement this. My idea is to maintain prices on an online database (for ex. Parse) so the game pings it to see if prices have changed.

My concern is what happens when someone is playing offline - they don't get the latest offers, sure, but is there a potential for someone to abuse the system by playing offline for an extended period when there is a certain offer open? How do you safeguard against that? Or do you just ignore and allow for it?

When offering daily specials/deals, do you use the system time on your device? Or the server time from the web? Again, is there potential for abuse here - i.e. by changing system time back 24 hours to reap more benefits.

Wondering how other games out there handle this. Thanks!