Describe what Unspent Transaction Outputs (UTXO) are.
All UTXOs of a bitcoin adress together are the available fund in your wallet you are able to spend.
What would happen if you don´t have any single UTXO that is large enough to cover your transaction?
A transaction could not be processed / accepted and will be rejected by the network when the total amount of all available UTXOs is lower than the desired transaction. Everytime a wallet creates a transaction, all UTXOs have to spend, the available funds that are not required for the transaction will be send back to original wallet as new UTXO.
How would a bitcoin wallet specify the transaction fee when creating a transaction?
The wallet is monitoring the transaction fees of latest transactions added to blockchain. It will choose automatically a transaction fee that results in the transaction being accepted by the miners in a reasonable amount of time. Transaction fees are calculated depending on digital length of transaction and not on amount of funds transferred. The higher the number of UTXOs (inputs) and the higher the number of outputs, the higher will be the transaction fee. Transaction fees are assesed in sat/B (fee(satoshies) per Bit). Current fees range between 1$ and 6$ USD.
How could you use the notion of transaction inputs and outputs to increase privacy in your transaction?
As all available UTXOs have always to be spend in a transaction, in most cases parts of the funds are transferred back to your own wallet. By even increasing the number of outputs going back to wallets owned by yourself. It is not possible to see from the outside how much of the fund have been transferred to an external wallet and how much of it went back to bitcoin adresses controlled by yourself