Yes, you have the payment outline in your contract, that is your invoice. The only additional invoice you should get is for upgrades and the extra work.

Yea, mostly we are putting together "draw requests" which are percentages of the total contract. Many banks do it for us by inspecting progress and determining the percentage task by task.

My first non bank job in 30 years and the client was upset my final bill was just "balance due" without progress detail line by line. I have to work on setting expectations.