Can my invoice show the amount paid and the balance due?

Yes, with a custom template. The template editor has fields for amount_paid, balance_due and payment_state:

1. Go to Settings → Store Settings → Invoice Templates and click New template, or Edit on your custom one.
2. Enter the Template name (required). Click the chips to insert amount paid, balance due and payment state near the total.
3. Click Save template, go back to Invoice Templates, and click Set active on it.

For Cash on Delivery, and for bank transfer or UPI until the proof is approved, the order counts as Unpaid. Amount paid is 0 and the balance is the full total. Fully paid orders show Paid, and an order with a part payment shows Partially paid.