Do I have to use contracts as the quantity unit when dealing with Futures?

I’m wondering if contracts are the only way to set the quantity units in futures.
Any alternatives?
On the site, we can send orders in terms of ADA.

If contracts are the only option, then how do I see how much available currency I can buy/sell in terms of contracts?

No, the quantity doesn’t have to follow in contracts term: https://binance-docs.github.io/apidocs/futures/en/#new-order-trade

You can test your orders to see how the API works with the Futures Testnet, consult more at https://binance-docs.github.io/apidocs/futures/en/#testnet

Read the link you sent. It mentions nothing of the /order endpoint and the quote-currency.
What do you think the quantity parameter is measured in?
Try it now - place an order. Set quantity to 1. Check if it’s in terms of the quote-currency or contracts.