DTI percentage is the percentage of your weekly income that is used to pay your expenses (expenses are broken down to weekly amounts to determine weekly cost). DSR is the debt servicability ratio which is the percentage of your income that is used to pay off your loans and credit cards. As a general rule banks etc will only lend money to people who have a DSR up to 37% or less.
A future week balance is the income due to be received in the week minus the expenses due to be paid. A negative value means more money is going out that week than coming in.