It's unlikely that you will find an API for free that has the same level of detail, ease of use and request parameter as the paid options. If you are only interested in the arriving flights at one airport, you could try scraping the website of the airport.
For example, the arrivals page of Heathrow makes the following request to their backend:
https://api-dp-prod.dp.heathrow.com/pihub/flights/arrivals?date=2023-12-10&orderBy=localArrivalTime&excludeCodeShares=true
If the request has the right headers set (cookie, content-type, etc...) this returns a neat JSON with 644 arriving flights with info on the airplane, the route, origin and destinations, etc.
You can find what calls are being made by opening the developer tools of your browser, going to the network tab and hitting refresh on the page of interest. Look for json-type calls or calls with a larger transferred payload:

Advantages:
- You can develop your webscraping skills (if you're into that)
- You might get more relevant information out of it than the API's (for your usecase)
- You don't have to pay money to someone else
Disadvantages:
- Huge timesink, you will have to reverse engineer the data schema, ensure that the calls keep on working when cookies expire, etc...
- Their backend API might change anytime
- You might get blocked due to recurring requests
- You probably need always on hardware to carry out periodic scraping
- You need to verify that the data you scrape matches the reality you want to investigate. E.g. if you're only interested in arriving flights you might need to manually exclude cancelled flights.
In summary I would only recommend this if:
- You don't value your time as much
- The paid API's don't deliver the data that you're looking for, but the scraped data does