Can the software keep track of which customers still owe me money for their trips?

Yes, travel agency software normally keeps a running record of what each customer has paid and what is still outstanding on every booking, so you can see at a glance who is behind without digging through your bank statements.

The way it usually works is that each booking holds a selling total, and any money you receive is recorded against that booking as a part payment or a deposit. The outstanding balance then updates on its own. If the customer pays by card on your portal, that payment is normally recorded automatically when it goes through. If they pay you in cash or by bank transfer, somebody on your team will need to enter it, because the software has no way of seeing your bank account by itself. You can then pull up a list of bookings with money still owing and work through it.

There are honest limits here. The software tracks balances, but it is not a full accounting system, so your bookkeeping will still live wherever it lives now. Payment due dates depend on the supplier and the fare or rate rules behind each booking, so a deadline shown against a booking is only as reliable as what the supplier sent. Whether you get automatic reminders to the customer, and how much of the layout you can change, often depends on the plan you are on and how your portal is set up.

Before you commit, write down the handful of things you actually need, such as part payments, a list of who owes what, and reminders, and ask to see each one working on a real booking during your demo.