The large coin is a 10-cash coin.
The other two are both 1-cash coins. The reason the small one is worth the same as a normal-size one is because China was in economic turmoil as a result of the abuse of the opium trade. Inflation occurred and the coins became very small.
The one with the raised rims, after looking at it once again, could be a damaged coin in that the rim was raised artificial means, auch as a spoon or hammer. But all cast Chinese coins made after 589 AD have low, flat rims that are the same height as the characters on the coin. Anything other than that can generally be assumed to be counterfeit.
The answer to your last question, actively collecting Chinese coins and easy access to reference materials greatly help in quick identification.