I have been playing the game Coin Dozer on my iPhone which is a free game. When I can no longer play without having to wait 30 seconds for a new coin, I just delete the game and reinstall, I have been receiving more coins than the original starting point. Are these coins from bonuses or am I being charged for them? I have not purchased more coins, that's why I delete then reinstall, so I don't have to buy coins.
You will know if you are being charged an in-app purchase fee for extra coins by checking your purchase history from within the Account Section of the iTunes App on your PC or Mac. Just log into the store, check your account, and look in your history. Even free purchases are listed, so you will see if you are being charged.
Ordinarily just noting that a password request for your Apple ID would be required for any purchases would be a good hint if you are being charged or not, but in your specific case because you are downloading the game each time from the App store and playing immediately, it may be that the stored credentials from when you downloaded the item are being kept valid - it will not re-ask you for your password for a small period of time (I think 15 minutes). It's hard to say, so you should just go and confirm.
As for specific gameplay details, I am not familiar with it, so I cannot comment.