Is it possible to create a platform by writing smart contracts on the Ethereum blockchain in which anyone can transact using any cryptocurrency and/or fiat? Perhaps the fiat can be converted internally into ether.
There are only three ways for ether to be created: (1) during the genesis block, (2) at each block as part of the block reward, and (3) at each block as part of the uncle reward (potentially).
Everything else is a transfer of ether from one account to another. The exchange of fiat for ether necessarily must take place outside of the chain.
For this reason I would say that it is impossible to build a smart contract system that deals with fiat in a fully
trustless way. In other words, there will always have to be some sort of outside (outside of the blockchain) confirmation that the fiat was received and the ether is being transferred as a result of that transfer.
Think about the genesis block. The system itself could not have confirmed the genesis block. The genesis block is a bootstrap. How could the system itself possibly know which accounts should be assigned how many initial ether?
you could check https://limepay.io ; Helping dapps users execute Ethereum transactions with credit card. It is not the exact thing you are asking for, but could be helpful if you have dapp running on ethereum.