What is the transaction fee for one transaction? What is the dollar equivalent for a transaction? Does the amount of XMR sent affect the fee?
The fees are calculated based on the transaction size in kB, not the transaction amount.
The transaction size depends mainly on the number of inputs you are spending, and the number of outputs you are generating.
A typical transaction would use one or two inputs (which you received from a previous transaction) and two outputs (one is the amount you are willing to spend, and the other is the change back to yourself).
I.e. If you own an output of 10 and spend 5, it will generate a transaction with one input of 10, one output of 5 to your recipient, and one output of 5 - fees (approx. 4.9976, see below) to yourself.
If you are trying to spend more XMR than a single outputs contains, you will use 2, 3, or more outputs as inputs for your transaction.
If you're sending to multiple recipients at a time with the CLI, you will generate one more output per extra recipient.
If you're sweeping a single output, aka sending the whole output to a recipient, fees excluded, you only generate one output.
Before upcoming bulletproofs, the typical 1 input / 2 outputs transaction, the fees should be around 0.0024XMR (with low priority) so $0.276 approximately and depending on the actual rate.