1. Describe what Unspent Transaction Outputs (UTXO) are.
UTXOs for a wallet are outputs from several other transactions that have been sent to the wallet in question but have not been spent i.e. have not been used as inputs to any other transactions from this wallet.
2. What would happen if you don’t have any single UTXO that is large enough to cover for your transaction?
The wallet will figure out the difference between the amount you are spending and the total amount of UTXOs that you have (i.e. the total amount that you have to spend) and construct the transaction in such a way that the amount of btc you want to send is sent and the remaining amount goes back as another UTXO to you (back to the same wallet).
3. How would a bitcoin wallet specify the transaction fee when creating a transaction?
The btc wallet software queries the blockchain and automatically chooses a fee that will get your transaction confirmed in a reasonable amount of time.
4. How could you use the notion of transaction inputs and outputs to increase privacy in your transaction?
Because the bitcoin network only uses the wallet address to specify where transaction inputs are coming from and where transaction outputs are going to, it becomes impossible to identify from whom exactly the wallet addresses belong to, hence preserving the privacy of the individuals transacting on the network. Therefore, by becoming a participant on the btc network, you can leverage this privacy preserving / anonymity feature and increase privacy in your transaction(s) 